EDA - Inteligencia Aritifical

Author

Miguel Ángel Pérez Vargas

Published

October 13, 2024

En el contexto actual, los algoritmos realizados con inteliegencia artificial se han vuelto esenciales para resolver una amplia variedad de problemas, desde la clasificación de imágenes hasta la predicción de patrones complejos. Cada uno de ellos tiene un rendimiento distinto dependiendo de múltiples factores, entre ellos el tipo de framework utilizado para implementarlo y el tipo de datos sobre los que se entrena el modelo. Este análisis busca explorar estas diferencias para entender cuál framework proporciona mejores tesultados, especialemtne en términos de precisión y tiempo de entrenamiento, al trabajar con datos tabulares.

Los datos tabulares son uno de los tipos más comunes de datos utilizados en el entrenamiento de modelos de inteligencia artificial. Se organizan en filas y columnas, donde cada columna representa una característica y cada fila una observación, tal como ocurre en una hoja de cálculo. Estos datos, pueden incluir características como la edad, el ingreso, la ubicación, entre otras, y son utilizados en diversas aplicaciones industriales y académicas.

Por lo tanto, el objetivo de este análisis es responder a la siguiente pregunta: ¿Qué framework ofrece mejores resultados en términos de precisión y tiempo de entrenamiento al trabajar con datasets tabulares?. Esta pregunta permitirá evaluar el rendimiento y la eficiencia de los diferentes frameworks, identificando cuál de ellos puede ser más adecuado según las características del problema y los datos disponibles.

Para comenzar, se carga la base de datos:

library(readxl)
dataset <- read_excel("~/Dataset/Dataset_IA_corte_II.xlsx")
View(dataset)

Con fines ilustrativos, se hace una vista preliminar con los primeros 10 registros del dataset:

library(knitr)
print(kable(head(dataset, 10)))


|Algorithm      |Framework    |Problem_Type |Dataset_Type |  Accuracy| Precision|    Recall|  F1_Score| Training_Time|Date                |
|:--------------|:------------|:------------|:------------|---------:|---------:|---------:|---------:|-------------:|:-------------------|
|SVM            |Scikit-learn |Regression   |Time Series  | 0.6618051| 0.6929447|        NA| 0.4426950|      4.978592|2023-03-08 11:26:21 |
|K-Means        |Keras        |Clustering   |Time Series  | 0.7443216| 0.4900292| 0.8766533| 0.4414046|            NA|2023-03-09 11:26:21 |
|Neural Network |Keras        |Clustering   |Image        | 0.8852037| 0.5948056| 0.9685424| 0.9644707|      3.282594|2023-03-10 11:26:21 |
|SVM            |Keras        |Clustering   |Text         | 0.8416477| 0.8424142| 0.8748388| 0.7041523|      4.041629|2023-03-11 11:26:21 |
|SVM            |Scikit-learn |Regression   |Tabular      | 0.7229514| 0.6856109| 0.3010956| 0.6456472|      3.603991|2023-03-12 11:26:21 |
|K-Means        |PyTorch      |Regression   |Image        | 0.6368133| 0.6255330| 7.4548096| 0.8865271|      3.006475|2023-03-13 11:26:21 |
|Neural Network |PyTorch      |Regression   |Text         | 0.9985623| 0.6366858| 0.3357948| 0.9014956|            NA|2023-03-14 11:26:21 |
|Neural Network |Scikit-learn |Regression   |Image        | 0.7130907| 0.6756681| 0.4803251| 0.5993146|      2.328345|2023-03-15 11:26:21 |
|SVM            |Keras        |Regression   |Time Series  |        NA| 0.8710099| 0.3416673| 0.8161708|      3.406453|2023-03-16 11:26:21 |
|Random Forest  |Keras        |Regression   |Text         | 0.5818119| 0.9352508|        NA| 0.8626737|      3.419905|2023-03-17 11:26:21 |

Esta base de datos, está compuesta por un total de 560 filas y 10 columnas:

dim(dataset)
[1] 560  10

El dataset en cuestión, contiene 10 variables diferentes, que se definen y clasifican según sus tipos en la siguiente tabla:

# Cargar las librerías necesarias
library(knitr)
library(kableExtra)

# Crear un dataframe con las variables, sus definiciones y el tipo de variable
variables <- data.frame(
  Variable = c("Algorithm", "Framework", "Problem_Type", "Dataset_Type", 
               "Accuracy", "Precision", "Recall", "F1_Score", 
               "Training_Time", "Date"),
  
  Definición = c("Algoritmo de aprendizaje automático utilizado.",
                 "Framework utilizado para implementar el algoritmo.",
                 "Tipo de problema abordado por el modelo.",
                 "Tipo de datos utilizado para entrenar el modelo.",
                 "Precisión del modelo.",
                 "Proporción de verdaderos positivos sobre los ejemplos predichos como positivos.",
                 "Proporción de verdaderos positivos sobre los ejemplos que son realmente positivos.",
                 "Media armónica de la precisión y el recall.",
                 "Tiempo requerido para entrenar el modelo (en segundos).",
                 "Fecha en que se realizó la ejecución del modelo."),
  
  Tipo = c("Cualitativa, nominal", "Cualitativa, nominal", "Cualitativa, nominal", 
           "Cualitativa, nominal", "Cuantitativa, continua", "Cuantitativa, continua", 
           "Cuantitativa, continua", "Cuantitativa, continua", 
           "Cuantitativa, continua", "Cualitativa, ordinal")
)

# Crear una tabla a partir del dataframe
kable(variables, format = "html", escape = FALSE, col.names = c("Variable", "Definición", "Tipo")) %>%
  kable_styling(full_width = F, position = "left") %>%
  add_header_above(c("Variables - Inteligencia Artificial Dataset" = 3))
Variables - Inteligencia Artificial Dataset
Variable Definición Tipo
Algorithm Algoritmo de aprendizaje automático utilizado. Cualitativa, nominal
Framework Framework utilizado para implementar el algoritmo. Cualitativa, nominal
Problem_Type Tipo de problema abordado por el modelo. Cualitativa, nominal
Dataset_Type Tipo de datos utilizado para entrenar el modelo. Cualitativa, nominal
Accuracy Precisión del modelo. Cuantitativa, continua
Precision Proporción de verdaderos positivos sobre los ejemplos predichos como positivos. Cuantitativa, continua
Recall Proporción de verdaderos positivos sobre los ejemplos que son realmente positivos. Cuantitativa, continua
F1_Score Media armónica de la precisión y el recall. Cuantitativa, continua
Training_Time Tiempo requerido para entrenar el modelo (en segundos). Cuantitativa, continua
Date Fecha en que se realizó la ejecución del modelo. Cualitativa, ordinal

Utilizando la función summary, se verifica que los tipos de datos correspondan a su respectiva columna:

summary(dataset)
  Algorithm          Framework         Problem_Type       Dataset_Type      
 Length:560         Length:560         Length:560         Length:560        
 Class :character   Class :character   Class :character   Class :character  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character  
                                                                            
                                                                            
                                                                            
                                                                            
    Accuracy        Precision          Recall          F1_Score     
 Min.   :0.5038   Min.   :0.4019   Min.   :0.3001   Min.   :0.4000  
 1st Qu.:0.6236   1st Qu.:0.5632   1st Qu.:0.4819   1st Qu.:0.5515  
 Median :0.7578   Median :0.7195   Median :0.6493   Median :0.7086  
 Mean   :0.8779   Mean   :0.8129   Mean   :0.7486   Mean   :0.8122  
 3rd Qu.:0.8824   3rd Qu.:0.8596   3rd Qu.:0.8404   3rd Qu.:0.8438  
 Max.   :9.7181   Max.   :9.7320   Max.   :9.3662   Max.   :9.3740  
 NA's   :39       NA's   :19       NA's   :20       NA's   :20      
 Training_Time          Date                       
 Min.   : 0.1032   Min.   :2023-03-08 11:26:21.07  
 1st Qu.: 1.2441   1st Qu.:2023-07-26 05:26:21.07  
 Median : 2.4347   Median :2023-12-12 23:26:21.07  
 Mean   : 2.9910   Mean   :2023-12-12 23:26:21.07  
 3rd Qu.: 3.8131   3rd Qu.:2024-04-30 17:26:21.07  
 Max.   :46.9856   Max.   :2024-09-17 11:26:21.07  
 NA's   :20                                        

Al estar todo correcto, no es necesario realizar ninguna conversión.

A continuación, se dará inicio a la revisión de valores faltantes o NA:

library(readr)
probs1 <- problems(dataset)
probs1_adjusted <- probs1
probs1_adjusted$row <- probs1$row - 1
probs1_adjusted
# A tibble: 0 × 4
# ℹ 4 variables: row <dbl>, col <int>, expected <chr>, actual <chr>

Mediante la combinación de las funciones, colSum() & is.na(), se realiza un conteo de los valores NA en cada columna de la base de datos:

colSums(is.na(dataset))
    Algorithm     Framework  Problem_Type  Dataset_Type      Accuracy 
            0             0             0             0            39 
    Precision        Recall      F1_Score Training_Time          Date 
           19            20            20            20             0 

De lo anterior, es evidente que los datos faltantes en el dataset, se encuentran presentes únicamente en las columnas correspondientes a variables cuantitativas.

Ahora, se contará el número total de datos NA en el dataset:

sum(is.na(dataset))
[1] 118

Al detectar 118 registros con datos faltantes, es pertinente realizar un tratamiento a todos ellos. Sin embargo, primero se generan varios gráficos para comprender con mayor claridad la situación del dataset. Estos gráficos también servirán posteriormente para realizar comparaciones una vez que los datos hayan sido tratados.

library(VIM)
aggr(dataset, col = c('navyblue','red'), numbers = TRUE, sortVars = TRUE, labels = names(dataset), cex.axis = .7, gap = 3, ylab = c("Proportion of Missingness","Missingness Pattern"))


 Variables sorted by number of missings: 
      Variable      Count
      Accuracy 0.06964286
        Recall 0.03571429
      F1_Score 0.03571429
 Training_Time 0.03571429
     Precision 0.03392857
     Algorithm 0.00000000
     Framework 0.00000000
  Problem_Type 0.00000000
  Dataset_Type 0.00000000
          Date 0.00000000

Con el mismo propósito, se generará un Missingness Map:

library(Amelia)
missmap(dataset, col = c("red", "blue"), legend = TRUE)

Gracias a este gráfico, se puede afirmar que sólo el 2% de los datos contienen valores NA.

Para dar inicio al tratamiento, se utiliza la función na.omit() para eliminar todas las filas con valores NA en el dataset:

dataset_limpio <- na.omit(dataset)

Se generan dos gráficos, uno con los datos originales y otro con los datos eliminados para la variable Accuracy:

library(ggplot2)

ggplot(dataset, aes(x = Accuracy)) +
  geom_histogram(fill = "red", color = "black", bins = 30) +  
  ggtitle("Original Data") +
  xlab("Accuracy") +
  ylab("Frequency") +
  theme_minimal()

ggplot(dataset_limpio, aes(x = Accuracy)) +
  geom_histogram(fill = "green", color = "black", bins = 30) +   
  ggtitle("Listwise Deletion") +
  xlab("Accuracy") +
  ylab("Frequency") +
  theme_minimal()

Se generan dos gráficos, uno con los datos originales y otro con los datos eliminados para la variable Precision:

library(ggplot2)

ggplot(dataset, aes(x = Precision)) +
  geom_histogram(fill = "red", color = "black", bins = 30) +  
  ggtitle("Original Data") +
  xlab("Precision") +
  ylab("Frequency") +
  theme_minimal()

ggplot(dataset_limpio, aes(x = Precision)) +
  geom_histogram(fill = "green", color = "black", bins = 30) +   
  ggtitle("Listwise Deletion") +
  xlab("Precision") +
  ylab("Frequency") +
  theme_minimal()

Se generan dos gráficos, uno con los datos originales y otro con los datos eliminados para la variable Recall:

library(ggplot2)

ggplot(dataset, aes(x = Recall)) +
  geom_histogram(fill = "red", color = "black", bins = 30) +  
  ggtitle("Original Data") +
  xlab("Recall") +
  ylab("Frequency") +
  theme_minimal()

ggplot(dataset_limpio, aes(x = Recall)) +
  geom_histogram(fill = "green", color = "black", bins = 30) +   
  ggtitle("Listwise Deletion") +
  xlab("Recall") +
  ylab("Frequency") +
  theme_minimal()

Se generan dos gráficos, uno con los datos originales y otro con los datos eliminados para la variable F1_Score:

library(ggplot2)

ggplot(dataset, aes(x = F1_Score)) +
  geom_histogram(fill = "red", color = "black", bins = 30) +  
  ggtitle("Original Data") +
  xlab("F1_Score") +
  ylab("Frequency") +
  theme_minimal()

ggplot(dataset_limpio, aes(x = F1_Score)) +
  geom_histogram(fill = "green", color = "black", bins = 30) +   
  ggtitle("Listwise Deletion") +
  xlab("F1_Score") +
  ylab("Frequency") +
  theme_minimal()

Se generan dos gráficos, uno con los datos originales y otro con los datos eliminagos para la variable Training_Time:

library(ggplot2)

ggplot(dataset, aes(x = Training_Time)) +
  geom_histogram(fill = "red", color = "black", bins = 30) +  
  ggtitle("Original Data") +
  xlab("Training_Time") +
  ylab("Frequency") +
  theme_minimal()

ggplot(dataset_limpio, aes(x = Training_Time)) +
  geom_histogram(fill = "green", color = "black", bins = 30) +   
  ggtitle("Listwise Deletion") +
  xlab("Training_Time") +
  ylab("Frequency") +
  theme_minimal()

Todos estos gráficos, demustran que la distribución de cada variable se mantiene igual, aún tras haber eliminados los datos faltantes.

Por supuesto, se genera un nuevo Missingness Map, con los datos NA eliminados:

library(Amelia)
missmap(dataset_limpio, col = c("red", "blue"), legend = TRUE)

Como se puede observer, se obtuvo un 0% de datos faltantes, por lo tanto, se puede afirmar que el tratamiento fue exitoso.

En el siguiente paso, se realizará el resumen estadístico inicial, utilizando por supuesto, el dataset limpio.

Se utiliza la función summary para mostrar las medidas de tendencia central y dispersión para cada variable:

summary(dataset_limpio)
  Algorithm          Framework         Problem_Type       Dataset_Type      
 Length:448         Length:448         Length:448         Length:448        
 Class :character   Class :character   Class :character   Class :character  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character  
                                                                            
                                                                            
                                                                            
    Accuracy        Precision          Recall          F1_Score     
 Min.   :0.5038   Min.   :0.4031   Min.   :0.3001   Min.   :0.4000  
 1st Qu.:0.6183   1st Qu.:0.5661   1st Qu.:0.4898   1st Qu.:0.5486  
 Median :0.7490   Median :0.7275   Median :0.6513   Median :0.7031  
 Mean   :0.8458   Mean   :0.8387   Mean   :0.7611   Mean   :0.8014  
 3rd Qu.:0.8698   3rd Qu.:0.8670   3rd Qu.:0.8365   3rd Qu.:0.8396  
 Max.   :9.7181   Max.   :9.7320   Max.   :9.3662   Max.   :9.3740  
 Training_Time          Date                       
 Min.   : 0.1032   Min.   :2023-03-10 11:26:21.07  
 1st Qu.: 1.2982   1st Qu.:2023-08-02 23:26:21.07  
 Median : 2.4809   Median :2023-12-24 23:26:21.07  
 Mean   : 3.0598   Mean   :2023-12-19 17:35:59.65  
 3rd Qu.: 3.8446   3rd Qu.:2024-05-07 05:26:21.07  
 Max.   :46.9856   Max.   :2024-09-17 11:26:21.07  

A su vez, se realiza la detección de outliers, para lo se crearán varios diagramas de caja y bigote que correspondan a cada variable numérica:

boxplot(dataset_limpio$Accuracy, ylab = "Accuracy")

boxplot(dataset_limpio$Precision, ylab = "Precision")

boxplot(dataset_limpio$Recall, ylab = "Recall")

boxplot(dataset_limpio$F1_Score, ylab = "F1_Score")

boxplot(dataset_limpio$Training_Time, ylab = "Training_Time")

Al todas las variables numéricas tener una cantidad significativa de valores atípicos, es necesario aplicar técnicas de limpieza o imputación:

Para ello, se utiliza la librería mice para crear un nuevo dataset con los outliers imputados.

variables_numericas <- c("Accuracy", "Precision", "Recall", "F1_Score", "Training_Time")

for (var in variables_numericas) {
  
  x <- dataset[[var]]
  
  qnt <- quantile(x, probs = c(.25, .75), na.rm = TRUE)
  H <- 1.5 * IQR(x, na.rm = TRUE)
  
  #se sacan los valores atípicos
  limite_inferior <- qnt[1] - H
  limite_superior <- qnt[2] + H
  
  mediana <- median(x, na.rm = TRUE)
  
  #Se realiza la imputación en base a la mediana
  x[x < limite_inferior] <- mediana
  x[x > limite_superior] <- mediana
  
  dataset[[var]] <- x
}

head(dataset)
# A tibble: 6 × 10
  Algorithm      Framework   Problem_Type Dataset_Type Accuracy Precision Recall
  <chr>          <chr>       <chr>        <chr>           <dbl>     <dbl>  <dbl>
1 SVM            Scikit-lea… Regression   Time Series     0.662     0.693 NA    
2 K-Means        Keras       Clustering   Time Series     0.744     0.490  0.877
3 Neural Network Keras       Clustering   Image           0.885     0.595  0.969
4 SVM            Keras       Clustering   Text            0.842     0.842  0.875
5 SVM            Scikit-lea… Regression   Tabular         0.723     0.686  0.301
6 K-Means        PyTorch     Regression   Image           0.637     0.626  0.649
# ℹ 3 more variables: F1_Score <dbl>, Training_Time <dbl>, Date <dttm>
library(mice)

imputacion <- mice(dataset[, c("Accuracy", "Precision", "Recall", "F1_Score", "Training_Time")], method = "pmm", m = 5, maxit = 50, seed = 500)

 iter imp variable
  1   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  1   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  1   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  1   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  1   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  2   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  2   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  2   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  2   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  2   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  3   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  3   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  3   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  3   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  3   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  4   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  4   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  4   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  4   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  4   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  5   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  5   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  5   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  5   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  5   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  6   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  6   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  6   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  6   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  6   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  7   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  7   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  7   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  7   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  7   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  8   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  8   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  8   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  8   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  8   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  9   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  9   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  9   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  9   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  9   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  10   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  10   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  10   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  10   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  10   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  11   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  11   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  11   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  11   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  11   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  12   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  12   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  12   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  12   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  12   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  13   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  13   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  13   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  13   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  13   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  14   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  14   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  14   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  14   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  14   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  15   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  15   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  15   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  15   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  15   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  16   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  16   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  16   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  16   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  16   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  17   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  17   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  17   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  17   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  17   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  18   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  18   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  18   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  18   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  18   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  19   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  19   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  19   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  19   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  19   5  Accuracy  Precision  Recall  F1_Score  Training_Time
  20   1  Accuracy  Precision  Recall  F1_Score  Training_Time
  20   2  Accuracy  Precision  Recall  F1_Score  Training_Time
  20   3  Accuracy  Precision  Recall  F1_Score  Training_Time
  20   4  Accuracy  Precision  Recall  F1_Score  Training_Time
  20   5  Accuracy  Precision  Recall  F1_Score  Training_Time
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dataset_imputado <- complete(imputacion)

dataset$Accuracy <- dataset_imputado$Accuracy
dataset$Precision <- dataset_imputado$Precision
dataset$Recall <- dataset_imputado$Recall
dataset$F1_Score <- dataset_imputado$F1_Score
dataset$Training_Time <- dataset_imputado$Training_Time

Se generan nuevamente los boxplots correspondientes a las variables numéricas, con el fin de verificar que el tratamiento haya funcionado:

boxplot(dataset$Accuracy, ylab = "Accuracy")

boxplot(dataset$Precision, ylab = "Precision")

boxplot(dataset$Recall, ylab = "Recall")

boxplot(dataset$F1_Score, ylab = "F1_Score")

boxplot(dataset$Training_Time, ylab = "Training_Time")

Como se puede apreciar, ya no se evidencian valores atípicos presentes en los diagramas de caja y bigote, por lo que se puede afirmar que la imputación de outliers funcionó correctamente.

Se analizan las variables categóricas. Para cada una de ellas, se saca su tabla de frecuencia, medidas de tendencia central, medidas de dispersión, curtosis y asimetría. Es importante anotar, que en las variables categóricas, no es posible verificar la distribución normal, pues las pruebas de normalidad, están reservadas para las variables cuantitativas o numéricas. Además, se omiten los diagramas de caja y bigote, pues fueron estudiados anteriormente.

Para Algorithm:

library(e1071)  
library(dplyr)  

variable <- dataset$Algorithm

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
barplot(frecuencia, main="Distribución de la Variable Algorithm", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
       K-Means Neural Network  Random Forest            SVM 
           163            135            126            136 
print(paste("Media:", media))
[1] "Media: 2.41964285714286"
print(paste("Mediana:", mediana))
[1] "Mediana: 2"
print(paste("Moda:", moda))
[1] "Moda: K-Means"
print(paste("Varianza:", varianza))
[1] "Varianza: 1.31374584717608"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 1.14618752705484"
print(paste("Rango:", rango))
[1] "Rango: 1" "Rango: 4"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.41816896675628"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0.100895122891551"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
25% 50% 75% 
  1   2   3 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 
  1   1   1   1   1   2   2   2   2   2   3   3   3   3   3   4   4   4   4 

Para Framework:

library(e1071)  
library(dplyr)  

variable <- dataset$Framework

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
barplot(frecuencia, main="Distribución de la Variable Framework", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
       Keras      PyTorch Scikit-learn   TensorFlow 
         124          135          134          167 
print(paste("Media:", media))
[1] "Media: 2.61428571428571"
print(paste("Mediana:", mediana))
[1] "Mediana: 3"
print(paste("Moda:", moda))
[1] "Moda: TensorFlow"
print(paste("Varianza:", varianza))
[1] "Varianza: 1.27850753897266"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 1.13071107670026"
print(paste("Rango:", rango))
[1] "Rango: 1" "Rango: 4"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.38315005467743"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: -0.124601550692842"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
25% 50% 75% 
  2   3   4 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 
  1   1   1   1   2   2   2   2   2   3   3   3   3   3   4   4   4   4   4 

Para Problem_Type:

library(e1071)  
library(dplyr)  

variable <- dataset$Problem_Type

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
barplot(frecuencia, main="Distribución de la Variable Problem_Type", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
Classification     Clustering     Regression 
           175            196            189 
print(paste("Media:", media))
[1] "Media: 2.025"
print(paste("Mediana:", mediana))
[1] "Mediana: 2"
print(paste("Moda:", moda))
[1] "Moda: Clustering"
print(paste("Varianza:", varianza))
[1] "Varianza: 0.650536672629696"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 0.806558536393792"
print(paste("Rango:", rango))
[1] "Rango: 1" "Rango: 3"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.46422623496655"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: -0.0452047551811593"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
25% 50% 75% 
  1   2   3 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 
  1   1   1   1   1   1   2   2   2   2   2   2   2   3   3   3   3   3   3 

Para Dataset_Type:

library(e1071)  
library(dplyr)  

variable <- dataset$Dataset_Type

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
barplot(frecuencia, main="Distribución de la Variable Dataset_Type", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
      Image     Tabular        Text Time Series 
        157         136         143         124 
print(paste("Media:", media))
[1] "Media: 2.41785714285714"
print(paste("Mediana:", mediana))
[1] "Mediana: 2"
print(paste("Moda:", moda))
[1] "Moda: Image"
print(paste("Varianza:", varianza))
[1] "Varianza: 1.24905443393815"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 1.11761103875103"
print(paste("Rango:", rango))
[1] "Rango: 1" "Rango: 4"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.36090786026508"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0.0791470485338742"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
25% 50% 75% 
  1   2   3 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 
  1   1   1   1   1   2   2   2   2   2   3   3   3   3   3   4   4   4   4 

Para Date:

library(e1071)  
library(dplyr)  

variable <- dataset$Date

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
  barplot(frecuencia, main="Distribución de la Variable Date", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
2023-03-08 11:26:21.08 2023-03-09 11:26:21.08 2023-03-10 11:26:21.08 
                     1                      1                      1 
2023-03-11 11:26:21.08 2023-03-12 11:26:21.08 2023-03-13 11:26:21.08 
                     1                      1                      1 
2023-03-14 11:26:21.08 2023-03-15 11:26:21.08 2023-03-16 11:26:21.08 
                     1                      1                      1 
2023-03-17 11:26:21.08 2023-03-18 11:26:21.08 2023-03-19 11:26:21.08 
                     1                      1                      1 
2023-03-20 11:26:21.08 2023-03-21 11:26:21.08 2023-03-22 11:26:21.08 
                     1                      1                      1 
2023-03-23 11:26:21.08 2023-03-24 11:26:21.08 2023-03-25 11:26:21.08 
                     1                      1                      1 
2023-03-26 11:26:21.08 2023-03-27 11:26:21.08 2023-03-28 11:26:21.08 
                     1                      1                      1 
2023-03-29 11:26:21.08 2023-03-30 11:26:21.08 2023-03-31 11:26:21.08 
                     1                      1                      1 
2023-04-01 11:26:21.08 2023-04-02 11:26:21.08 2023-04-03 11:26:21.08 
                     1                      1                      1 
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2024-08-11 11:26:21.08 2024-08-12 11:26:21.08 2024-08-13 11:26:21.08 
                     1                      1                      1 
2024-08-14 11:26:21.08 2024-08-15 11:26:21.08 2024-08-16 11:26:21.08 
                     1                      1                      1 
2024-08-17 11:26:21.08 2024-08-18 11:26:21.08 2024-08-19 11:26:21.08 
                     1                      1                      1 
2024-08-20 11:26:21.08 2024-08-21 11:26:21.08 2024-08-22 11:26:21.08 
                     1                      1                      1 
2024-08-23 11:26:21.08 2024-08-24 11:26:21.08 2024-08-25 11:26:21.08 
                     1                      1                      1 
2024-08-26 11:26:21.08 2024-08-27 11:26:21.08 2024-08-28 11:26:21.08 
                     1                      1                      1 
2024-08-29 11:26:21.08 2024-08-30 11:26:21.08 2024-08-31 11:26:21.08 
                     1                      1                      1 
2024-09-01 11:26:21.08 2024-09-02 11:26:21.08 2024-09-03 11:26:21.08 
                     1                      1                      1 
2024-09-04 11:26:21.08 2024-09-05 11:26:21.08 2024-09-06 11:26:21.08 
                     1                      1                      1 
2024-09-07 11:26:21.08 2024-09-08 11:26:21.08 2024-09-09 11:26:21.08 
                     1                      1                      1 
2024-09-10 11:26:21.08 2024-09-11 11:26:21.08 2024-09-12 11:26:21.08 
                     1                      1                      1 
2024-09-13 11:26:21.08 2024-09-14 11:26:21.08 2024-09-15 11:26:21.08 
                     1                      1                      1 
2024-09-16 11:26:21.08 2024-09-17 11:26:21.08 
                     1                      1 
print(paste("Media:", media))
[1] "Media: 280.5"
print(paste("Mediana:", mediana))
[1] "Mediana: 280.5"
print(paste("Moda:", moda))
[1] "Moda: 2023-03-08 11:26:21.08"
print(paste("Varianza:", varianza))
[1] "Varianza: 26180"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 161.802348561447"
print(paste("Rango:", rango))
[1] "Rango: 1"   "Rango: 560"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.20643045741024"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
   25%    50%    75% 
140.75 280.50 420.25 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
    5%    10%    15%    20%    25%    30%    35%    40%    45%    50%    55% 
 28.95  56.90  84.85 112.80 140.75 168.70 196.65 224.60 252.55 280.50 308.45 
   60%    65%    70%    75%    80%    85%    90%    95% 
336.40 364.35 392.30 420.25 448.20 476.15 504.10 532.05 

Ahora, se analizan las variables numéricas. En este caso, también se omiten los diagramas de caja y bigote.

Para Accuracy:

library(e1071)  
library(dplyr)  

variable <- dataset$Accuracy

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
  hist(frecuencia, main="Distribución de la Variable Accuracy", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
0.503781437489071 0.504885423709592 0.505515632214324  0.50581026995405 
                1                 1                 1                 1 
0.509116291338181 0.509596138411528 0.511819293023168 0.512821032903218 
                1                 1                 1                 1 
0.512905953474744 0.514986794936339 0.515193529848418 0.515326251102903 
                1                 1                 1                 1 
0.515567041442256 0.515793072412821 0.516601554395683 0.518080190262381 
                1                 1                 1                 1 
0.518335713466771 0.519671770334255 0.519809412674179 0.520786429525196 
                1                 1                 1                 1 
 0.52170626642741 0.524106019430278 0.528543428044657 0.528890280498183 
                1                 1                 2                 1 
0.529081897752738 0.530071171300393  0.53013369514478 0.530176041995282 
                3                 4                 1                 1 
0.530674813555334 0.531145899065031 0.532104468537567 0.533806281796107 
                1                 1                 1                 1 
0.534086154692747 0.534711921373047 0.536099204489588 0.536223443897279 
                1                 1                 2                 1 
0.536597961884222  0.53928924857751 0.539709684494493 0.540057423192338 
                2                 1                 1                 1 
0.540459641525626 0.541190522807921 0.542829124798215 0.543821373381919 
                1                 1                 1                 1 
0.543933249572417 0.544562216058008 0.547767656917334 0.547857277760081 
                1                 1                 1                 1 
 0.54833822482336 0.549041290392122 0.550522905505323 0.550710414224608 
                1                 1                 1                 1 
0.552054824692083   0.5522839201672 0.552465089209087 0.552832342130872 
                1                 1                 1                 1 
0.553296515153995 0.554868099338752 0.555959809698864 0.558183198942738 
                1                 1                 1                 1 
0.558654094481197 0.560104527685304 0.560692469711214 0.560943046668474 
                1                 1                 1                 2 
0.561054957005013 0.562592896101275 0.563856741817617 0.564197144727063 
                1                 1                 1                 1 
  0.5653551883701 0.565436830359175 0.565622438841194 0.566262336370924 
                1                 2                 1                 1 
 0.56635787702153 0.567583144577411 0.568219876278367 0.568554852864499 
                1                 1                 1                 1 
0.569825627378156 0.571124684343598 0.571247771450757 0.573186996081125 
                1                 1                 1                 1 
 0.57552894589045 0.576012426564324 0.576208006665209 0.579772340056594 
                1                 2                 1                 1 
0.581761936292511 0.581811910595835 0.583520953950475 0.583741291129535 
                3                 1                 1                 1 
0.583809608144159 0.584007103872432  0.58487895254377 0.586762257493254 
                1                 3                 1                 1 
0.587419313630206  0.58765147117883 0.588574894723693 0.589841554435121 
                1                 1                 1                 1 
0.590488476354745  0.59057467476734 0.590719173847813  0.59105895784435 
                1                 1                 1                 1 
0.595933662359371 0.597311255910383 0.599771225464573 0.600075122122405 
                1                 1                 1                 1 
0.600262363350168 0.600466844329528 0.600926726061474 0.602920605018384 
                2                 1                 1                 1 
0.604255257178668 0.606022419954113 0.607600936008619 0.607837576198859 
                1                 1                 1                 2 
  0.6080190912548 0.608369900045388 0.609606993679022  0.61038480639438 
                1                 1                 1                 1 
0.613328201113494 0.613634813631576 0.614039885974466 0.614977302945543 
                1                 1                 1                 1 
0.615973548057988 0.616856040955217 0.617321040927727 0.618025231673232 
                1                 1                 1                 1 
0.618435279487241 0.618771662461939 0.619590052107963 0.620600728799771 
                1                 1                 1                 1 
0.621022507931264 0.623551617005073 0.623615537201589 0.624357136293815 
                1                 1                 1                 1 
0.628281391850682 0.628388283860254 0.629906604372517 0.631556284955421 
                1                 1                 1                 1 
0.634496702217549 0.634874805758495 0.636312000366767 0.636629763499105 
                1                 1                 1                 1 
0.636813333140833 0.637080333279903 0.637107601174335 0.637403017774068 
                2                 1                 1                 1 
0.638413898617526 0.642436450980961 0.645831289354652 0.651564177972664 
                1                 1                 1                 1 
0.651637573783798  0.65233956954902 0.652762155329012 0.653126810393306 
                1                 1                 1                 1 
0.653644982463143 0.653964970795595 0.655180979461787 0.655653849578002 
                1                 1                 1                 1 
 0.65590806654263 0.658078052488375  0.66168578105776 0.661805109574771 
                1                 1                 1                 1 
0.662166876557688 0.662292914950135 0.662595032112347 0.663230654121996 
                1                 1                 1                 1 
0.663516580781619 0.666500956529099 0.668447895885553 0.668501588215643 
                1                 1                 1                 1 
0.669725096271403 0.670623913813078 0.673049863268893 0.673785762119491 
                1                 1                 1                 1 
 0.67531346560459 0.675811343619817 0.676710689651359 0.677498152915969 
                1                 1                 1                 1 
0.679616684699883 0.680068203735759 0.683230767435699 0.683767211145766 
                1                 1                 2                 1 
0.683879675438645 0.684263171861881 0.685519381492301  0.68662589581467 
                1                 1                 1                 1 
0.689892890089615  0.69031164673829 0.694279050635173 0.695452997952757 
                1                 1                 2                 1 
 0.69554076832588 0.696246778203342 0.696932202827079 0.698086345804628 
                1                 1                 1                 1 
0.698461638100798 0.698490758537142 0.698797198981397 0.699331513886157 
                1                 1                 1                 1 
 0.69941139044845 0.699657957904654 0.701490089382581 0.702070160825516 
                1                 1                 1                 1 
0.702159384052146 0.703453980361435 0.704667003157522 0.705514234903352 
                1                 1                 1                 1 
0.706774550762676 0.707064876264464 0.708076999089881 0.709863658463061 
                1                 1                 1                 1 
0.710860463436728 0.711869126824381 0.713041691945186 0.713090651117986 
                1                 1                 1                 1 
0.714099807462807 0.715152947449731 0.716167400521301 0.716248939165066 
                1                 1                 1                 1 
0.717791657406466 0.719307709594795 0.719755844316455 0.721875109652286 
                1                 1                 1                 1 
0.722652627501333 0.722951353188374 0.723601270252418 0.724346811311265 
                1                 1                 1                 1 
0.726099514141718  0.72615914225915  0.72718866727998  0.72736992781693 
                1                 1                 2                 1 
0.727610074540901  0.72990021188466 0.731311478369658 0.731747021900286 
                1                 1                 1                 1 
0.732602806141859 0.736604953345779 0.737315437874907 0.739590938814865 
                1                 1                 1                 1 
0.739969417358562 0.740253473628914 0.740672075817662 0.740761175756275 
                1                 1                 1                 1 
0.741772823359962 0.742935879593163 0.743334470712351 0.743530959409468 
                1                 1                 1                 1 
0.743927021963181 0.744321595202333  0.74442329012846 0.745797273370718 
                1                 1                 1                 1 
0.746138928224017 0.748383429429585 0.748481741452915 0.748587382004214 
                1                 1                 1                 1 
0.749097858226569 0.749444076725678 0.751283038231721 0.753070931420122 
                1                 1                 1                 1 
0.753617404344196 0.754711064074895 0.757408676964845 0.757798014289625 
                1                 1                 1                 2 
0.757839713848249 0.758855821692356 0.759529895454135 0.759540892568109 
               11                 1                 1                 1 
0.759886974278009 0.760478988636021  0.76258169183353 0.763201330468057 
                1                 1                 1                 1 
0.763520731955826 0.765584764000516 0.766478893275668 0.766801273363439 
                1                 1                 1                 1 
0.767655065726296 0.767913842236541 0.769580638337627  0.76997856514028 
                1                 1                 1                 1 
0.770005957302255 0.770648167650535 0.772244548980425 0.773348706357035 
                1                 1                 1                 1 
0.773796188076868 0.773979744486846 0.774764767947508 0.775113271078131 
                1                 1                 1                 1 
0.776901120356188 0.777681775468816 0.778891708685012 0.779824341743457 
                1                 1                 1                 1 
0.781148407938955 0.783508130493334 0.783656109814452 0.783770424130779 
                1                 1                 1                 1 
0.785304873319415 0.789193458503205 0.789337704286197 0.790985700957199 
                1                 1                 1                 1 
0.792677182198376 0.793304231587737 0.796175164296681 0.796475425717464 
                1                 1                 1                 1 
0.797238167593087 0.800010274059652 0.800297166680309 0.800805910073166 
                1                 1                 1                 1 
0.801724296690689 0.803126468875489  0.80354701804439 0.803952546396722 
                3                 1                 1                 1 
0.805166891655459 0.805490494425496 0.807609719115505 0.808325157260369 
                2                 1                 1                 1 
0.808572493302015 0.808923620100607 0.809077867159059 0.809745173004807 
                1                 1                 1                 1 
0.809793977448915 0.811483291781741 0.811929662338287 0.811947918145819 
                1                 1                 1                 1 
0.813110160815708  0.81578011004626 0.816575687797011 0.818215124771818 
                1                 1                 1                 1 
0.819262973832043  0.81955996890775 0.820413157345103 0.820486038672666 
                1                 1                 1                 1 
0.820985750221633 0.821788847598262 0.823737357077301 0.825100546199077 
                1                 1                 1                 1 
0.825162843173468 0.825438684523597 0.825616488520746 0.825833412687943 
                1                 1                 1                 1 
0.828368332270646 0.828922652301518 0.829353887750438 0.831902263810903 
                1                 1                 1                 1 
0.832455862243609 0.833432128773052 0.833774949645735 0.833796692781792 
                1                 1                 1                 1 
0.834106399277508 0.834743477599095 0.836301059112563 0.836716216662459 
                1                 1                 1                 1 
0.838256692888623 0.840114121215646 0.840249651037356 0.841624014144823 
                1                 1                 1                 1 
0.841647688303253 0.842782643614486 0.844732484568633 0.844763375515781 
                1                 1                 1                 1 
0.846080670847066 0.846218075662185 0.846312976113082 0.846841112890744 
                1                 1                 1                 1 
0.847475544451231 0.847490943063271 0.847517614429277 0.851232485272052 
                1                 1                 1                 1 
0.852340381368323 0.853388608442723 0.854372348871488 0.854523130861216 
                2                 1                 3                 1 
0.854530259725458 0.857043466066214 0.858075337111597 0.858798882829088 
                1                 1                 1                 1 
0.859061538113247 0.859600889136132 0.862169408564371 0.862628830207568 
                1                 1                 1                 2 
0.863584534883154 0.865325255119623 0.865794760877666 0.866556511207641 
                1                 1                 1                 1 
0.866807190280701  0.86820100753282 0.868436872472091 0.869224604625663 
                1                 1                 1                 1 
0.871353260599991 0.877635210248404 0.878081664447623 0.880144911561068 
                1                 2                 1                 1 
0.880511995471499 0.881142567388308 0.882404900451498 0.882441630771064 
                1                 4                 1                 1 
 0.88465244682067 0.885203708903897 0.885460922322026   0.8867365628433 
                1                 1                 1                 1 
0.888298426395871 0.889925494446675 0.890262757621931  0.89038079303422 
                1                 1                 1                 1 
0.891014043835193 0.891192742029137  0.89484925357124 0.895015218153531 
                1                 1                 1                 1 
0.897404774374965 0.897724980394865 0.898268645488088 0.898779550318594 
                1                 1                 1                 1 
0.898906824429317 0.900178253911181 0.900293349554541 0.900768555941495 
                1                 1                 1                 1 
0.900864041534896 0.901512948916332 0.902835076475027 0.902996274887579 
                1                 1                 1                 1 
0.903922970970629 0.906492869358047 0.906985134753009 0.908648884981247 
                1                 1                 1                 1 
0.908724854245596 0.908917108087511 0.909594429713395 0.911240281817181 
                1                 1                 2                 1 
0.911307159256839 0.913033815126264 0.913768947783437 0.914441682941305 
                1                 1                 1                 1 
 0.91993065143336 0.921016647188211 0.922085224484599 0.922178541369808 
                1                 1                 1                 1 
0.922391614058444 0.925712478872548  0.92719254668479 0.930061198594602 
                1                 1                 1                 1 
0.931007241136311 0.931398538771614 0.931666824785913 0.933959147260011 
                1                 1                 1                 1 
0.934028345053725 0.934071127188753 0.934135640256629  0.93413625270419 
                1                 1                 1                 1 
0.934311583977805 0.934452492239359 0.935374950636256  0.93537672516863 
                1                 2                 1                 1 
0.935484561873043 0.935891783296101  0.93671161904083 0.938987160222535 
                1                 1                 1                 1 
0.939257780650674 0.940039543780729 0.942103231674204 0.943302107620233 
                1                 1                 1                 1 
0.947049601839567 0.947095437332059 0.947408328030264 0.950011561699006 
                1                 1                 1                 1 
0.950350932005629 0.954516260332821 0.956181672808345 0.959695986607209 
                1                 1                 1                 1 
0.960423923907843 0.961378595256697 0.963500483962148 0.963517272398153 
                1                 1                 1                 1 
0.963588909739726 0.965297607321958 0.965474347753489 0.966937508763952 
                3                 1                 1                 1 
0.967218013402757 0.968106123121845 0.968302846147481 0.968478911515531 
                1                 1                 1                 1 
0.972307109737012 0.975431781125205 0.975701671103329  0.97590589271162 
                1                 1                 1                 1 
0.977761847977467  0.97881264225269 0.979788322160517  0.98146343761879 
                1                 1                 1                 1 
0.981557555794587 0.982559348218023  0.98291108057661 0.984096713957361 
                1                 1                 1                 1 
0.984706161167644 0.984910522539272 0.984956023053635  0.98569754702082 
                1                 1                 1                 2 
0.987396581073392 0.987805100429958 0.987932627909566 0.987936877455027 
                1                 1                 1                 1 
0.988587092110659 0.991839462631707 0.991988823979914 0.993315061479424 
                1                 1                 1                 1 
0.993331296633573 0.993892760107444 0.995627996851094 0.996079007411656 
                1                 1                 1                 1 
0.996241751079188 0.997069680610584 0.997433158584884 0.998166958028371 
                1                 2                 1                 1 
0.998348426926488 0.998562250078856 0.999706862885333 
                1                 1                 1 
print(paste("Media:", media))
[1] "Media: 253.894642857143"
print(paste("Mediana:", mediana))
[1] "Mediana: 259.5"
print(paste("Moda:", moda))
[1] "Moda: 0.757839713848249"
print(paste("Varianza:", varianza))
[1] "Varianza: 21859.579219908"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 147.849853635058"
print(paste("Rango:", rango))
[1] "Rango: 1"   "Rango: 511"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.20613295365698"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0.00583851473392025"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
   25%    50%    75% 
123.75 259.50 381.25 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
    5%    10%    15%    20%    25%    30%    35%    40%    45%    50%    55% 
 25.95  48.90  74.85  97.80 123.75 150.70 178.65 204.60 231.55 259.50 276.45 
   60%    65%    70%    75%    80%    85%    90%    95% 
304.40 329.35 357.30 381.25 405.20 432.15 459.10 485.05 

De este histograma, se infiere que la distribución de esta variable no es normal, y además, está sesgada hacia la derecha.

Para Precision:

library(e1071)  
library(dplyr)  

variable <- dataset$Precision

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
  hist(frecuencia, main="Distribución de la Variable Precision", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
0.401930958162567 0.403137768125748 0.403303479496253 0.404598419589535 
                1                 1                 1                 1 
0.407442421766389 0.410803933360273 0.412566976618548 0.413094038065294 
                1                 1                 1                 1 
0.415718025119239 0.416300452735336 0.419913612737456  0.42016816010997 
                1                 1                 1                 1 
 0.42080216003589 0.421186812964144 0.422032817500493 0.423055809377395 
                1                 1                 1                 2 
0.425003740361431 0.425170734058982 0.425214805102843 0.425904241478207 
                1                 1                 2                 1 
 0.42738924730143 0.428885701587012 0.431173946532561 0.431354727571614 
                1                 1                 1                 1 
0.435130557546388 0.437363863529131 0.437591922073213 0.438184545571985 
                1                 1                 1                 1 
0.438912156689781 0.439122754756295 0.439219694538631 0.439991224336414 
                1                 1                 1                 1 
0.440601017140001 0.441374809813853 0.441784688897443 0.442559329680264 
                1                 1                 1                 1 
0.442754036659155 0.443250601599204 0.447381497314497 0.447643950785818 
                1                 1                 1                 1 
0.448360908254275 0.449035207448067 0.449303000485856  0.45007845099363 
                1                 1                 1                 1 
0.450875209627482 0.452255660077463  0.45316025780777 0.455794383893879 
                1                 1                 1                 1 
0.456314370894014 0.457920682117264 0.459037389828038  0.45950685975233 
                1                 1                 1                 1 
 0.46038248711412 0.462534881685009 0.463284219973978 0.464815452478415 
                1                 1                 1                 1 
0.466593681528089 0.467548234247162 0.468303036085961  0.46845747093276 
                1                 1                 1                 1 
0.468861323121531  0.46895979823574 0.471001714554032 0.472831850895644 
                1                 1                 1                 1 
0.472900825780551 0.475758844938702  0.47685744781972 0.478893471938789 
                1                 1                 1                 1 
0.479037264072737 0.480087983449566 0.481212449366611 0.483547222670557 
                1                 1                 1                 1 
0.484014458531991 0.484426916829255 0.485183193856596  0.48847151602377 
                1                 1                 1                 1 
0.489332830199467 0.490029198816391 0.490101400490225 0.490748097240961 
                1                 1                 1                 1 
0.491262569933364 0.494772893701209 0.495344900601612 0.496042980972744 
                1                 2                 1                 1 
0.497340043469488 0.498823812059377 0.498888889437662 0.499464724097965 
                1                 1                 1                 1 
0.499572937177471 0.504256955881446 0.504465601200451 0.506457261681824 
                1                 1                 1                 1 
0.510534903542816 0.510685751880184 0.511117340720481 0.511198107717229 
                1                 1                 1                 1 
0.511660850707766 0.512447166458549  0.51281484076925 0.517658627643036 
                1                 1                 1                 1 
0.518482293915962 0.518858579655844 0.520818269281585 0.521209401041494 
                1                 2                 1                 1 
0.521488336099142 0.522259875476613 0.522421380777339 0.523412357317333 
                1                 1                 1                 1 
0.524195547063056 0.528106819786403 0.531441285461115 0.532367171626727 
                1                 1                 1                 1 
0.534769367106311 0.535190157970741 0.536307734214109 0.542460081024884 
                1                 1                 1                 1 
0.543706101945723 0.543924467653567 0.544415627099503 0.545136296955303 
                1                 1                 1                 1 
0.548007318712974   0.5481872794432 0.549727719909704 0.550579996804179 
                1                 2                 1                 1 
0.551344612104017 0.552634948505108 0.552802373227631 0.553918037466549 
                1                 1                 1                 1 
0.555172500932823 0.555578055319464 0.556094674577231 0.556172114539602 
                1                 1                 1                 1 
0.557023410241544 0.559027856995002 0.561892432076929 0.563169835677179 
                1                 1                 1                 1 
0.563842485983687 0.564838915311712 0.566088584674784 0.566142692426685 
                1                 1                 1                 1 
0.567565653072646 0.568409929309585 0.568912719048958  0.56931224481592 
                1                 1                 1                 1 
0.571544073543496 0.572282774850745 0.575330938277139 0.575693222020579 
                2                 1                 1                 1 
0.577266866486452 0.577921348772593  0.57834268462517 0.578529070791292 
                1                 1                 2                 1 
0.579235344153264 0.579951466904191    0.580759156456 0.582367840744434 
                1                 1                 1                 1 
 0.58285065723168 0.583186406018039 0.583362529294129 0.588610067910249 
                1                 1                 1                 1 
0.589244137448808 0.590167952674672 0.594805556134036 0.595062409259019 
                1                 1                 1                 1 
0.596158969802847 0.596915652165587 0.598129038922899  0.59880820426183 
                1                 1                 1                 1 
0.600542991217637 0.600706773245159 0.601124828422524 0.602960503596699 
                1                 1                 1                 1 
0.603316389603251 0.607133885681015 0.608405995755306   0.6087648469493 
                1                 1                 1                 1 
0.609703823252091  0.60982193784751 0.611424967965793 0.611950845101239 
                2                 1                 1                 1 
0.613230741211444 0.613295806264814 0.614678959195265 0.617111855923083 
                1                 1                 1                 1 
0.617341264991373 0.620985718304109 0.623300214302508 0.625532971087462 
                1                 1                 1                 1 
0.628240329382246 0.628252004504537 0.629163783791738 0.630299771159826 
                1                 1                 1                 1 
0.630706796586888 0.634915418906698 0.636685767142021 0.636745645358588 
                1                 1                 1                 1 
0.637582283597473 0.638209024742315 0.640896589516773 0.645942933817773 
                1                 1                 1                 1 
0.646612645159327 0.647059324950705 0.647573104509174  0.65065658756506 
                1                 1                 1                 1 
0.651275991444497 0.652748831976443 0.653096907123299 0.653529056987167 
                1                 1                 1                 1 
0.656493812752369 0.657794087643361 0.658256446192594 0.659246129766518 
                1                 1                 1                 1 
0.660411619704325 0.660757576515227 0.662110421569108 0.662561874433235 
                1                 1                 1                 1 
0.663642993816671 0.664119398773294 0.664194051021009 0.666028008627513 
                1                 1                 1                 1 
0.668233326283855 0.669166378572726 0.669843905470324 0.670210587343248 
                1                 1                 1                 1 
0.670743606508593 0.674912132042736 0.674980384917194 0.675543926558175 
                1                 1                 1                 1 
0.675559118303928 0.675668061043592 0.676214962721156 0.676323698364484 
                1                 1                 1                 1 
0.676886478774841 0.676934484651874   0.6783588260874 0.678359492013002 
                1                 1                 1                 1 
0.681260779278704 0.682700739359689 0.682772300438899 0.683496013003908 
                1                 1                 1                 1 
 0.68561087762126 0.688583733931674 0.689224634867249 0.689781323251213 
                1                 2                 1                 1 
0.692542716204031 0.692600241172759 0.692944682213067 0.696127948204071 
                1                 1                 1                 1 
 0.69652746835018  0.69787669141318 0.698687504820574 0.698953409358072 
                1                 1                 1                 2 
0.703124064145983 0.703511615771097 0.703759635697122 0.705016328149768 
                1                 1                 1                 1 
0.707333152487605 0.707418266527474 0.707501589262199 0.707592851887032 
                1                 1                 1                 1 
0.709943577067587 0.710361433864966 0.710467811053025 0.710847259743289 
                1                 1                 1                 1 
0.711044813167123 0.711631515702362 0.713997778716845  0.71403454682462 
                1                 1                 1                 1 
0.716439773273606 0.718181279949495  0.71945240936513 0.719817320347684 
                1                 1                11                 1 
0.723221078771629 0.724419085986946 0.724476252991327 0.725342323295109 
                1                 1                 1                 1 
0.726122930405588 0.727016151338163 0.727259121644143 0.727988932112673 
                1                 1                 1                 1 
 0.73253590847921 0.733050969581372  0.73585341018303 0.736100910077105 
                1                 1                 1                 1 
0.736264378588264 0.736396056649703 0.736733672969515 0.736890752775714 
                1                 1                 1                 1 
 0.73901319571541 0.739198152742966 0.743063411228993 0.743123362736312 
                1                 1                 1                 1 
0.743229186021581 0.746556019528694 0.749453594924348 0.749684101050094 
                1                 1                 1                 1 
0.752661616517319 0.752921360169034 0.754208614275264 0.755018297383795 
                1                 1                 1                 1 
0.755826600512071 0.755932942064431 0.758935176438243 0.759014490578655 
                1                 1                 1                 1 
0.759387104906326 0.760390639929013 0.761128953781793 0.761154058609079 
                1                 1                 1                 1 
0.762092599957873 0.764253747231253 0.764743128454422  0.76511636361788 
                1                 1                 1                 1 
0.766135089686585 0.767763749496715 0.768360150856037  0.76900778082332 
                1                 1                 1                 1 
0.769178815041881 0.769591270156107 0.770239909670681 0.771753602475904 
                1                 1                 1                 1 
0.772557140487059 0.774798141312558 0.778784531855193 0.780462418825799 
                1                 1                 1                 2 
0.780485282977442 0.780749450530182 0.780802763952365  0.78170641882494 
                1                 1                 1                 1 
0.781774812387549 0.782001809300324 0.782320886084968 0.785395315543136 
                1                 1                 1                 1 
0.785539119721115 0.785729146035225 0.786342552124678 0.787486487593124 
                2                 1                 1                 1 
0.790584080290573 0.790688550929004 0.791334555727284  0.79189767431877 
                1                 1                 1                 1 
0.792504760884445 0.792575531394977 0.793697102608643 0.793887164398902 
                1                 1                 1                 1 
0.794068062834576 0.794173093760284  0.79561235332347 0.796181631820803 
                1                 1                 1                 1 
0.796822366642249 0.798273811705353 0.798990942085597 0.800682809935844 
                1                 1                 1                 1 
0.800751999282176 0.801413402397465 0.801520157762847   0.8024393871435 
                1                 1                 1                 1 
 0.80570653724526 0.805880762335817 0.808136667525012 0.811796318011659 
                1                 1                 1                 1 
0.812880823651925 0.813331181230054 0.816490344105899 0.817370887898084 
                2                 1                 1                 1 
0.817539470901282 0.821355259618999  0.82158026385131 0.822211586476477 
                1                 1                 1                 1 
0.824608560844549 0.824701058337861 0.826145679173987 0.827208412198468 
                1                 1                 1                 1 
0.828419586680114 0.829794032837609 0.831612173421495 0.833242562921642 
                1                 1                 1                 1 
 0.83368858192509 0.835587945991177 0.836002595242194 0.836763584184259 
                1                 1                 1                 1 
0.837094406296968 0.837704937191438 0.838492578988438 0.838897894204217 
                1                 1                 1                 1 
 0.83968092685975 0.839842777617805 0.841397868543514  0.84241424643268 
                1                 1                 1                 1 
0.842460261232891 0.842505015675404 0.843942472460158 0.845915919238962 
                1                 1                 1                 1 
0.846156349705936 0.847440269638739 0.848843907657719 0.849295802177984 
                1                 1                 1                 1 
0.850825051617427  0.85237714215807 0.853025157247767 0.854050903413181 
                1                 1                 1                 1 
0.855638957450778 0.856594456016856 0.856672922225895 0.858623597333042 
                1                 1                 1                 1 
0.859307739394666 0.859638865921182  0.86153388870288 0.863207485785994 
                1                 1                 1                 1 
0.864327793438094 0.864780268382673 0.864792118708709 0.865367110555197 
                1                 1                 1                 1 
0.865868467899835 0.866026334173109 0.870275070691238 0.870938186266881 
                1                 1                 1                 1 
0.871009926302234 0.871390970848139  0.87176691963042 0.872142031753177 
                1                 1                 1                 1 
0.873068405951979 0.873168978803444 0.875712651420304 0.875956810262953 
                1                 1                 1                 1 
0.876518398766251 0.876746967220114 0.878748495769536 0.879228514992745 
                1                 1                 1                 1 
0.880042581219496 0.881551407747888 0.881585985877426 0.882162121264921 
                1                 1                 2                 1 
0.882944066104863 0.882993399808462 0.883842170339704 0.887061872854083 
                1                 1                 1                 1 
 0.88956816338117 0.890671197914167 0.891438108316994 0.892982138626283 
                1                 1                 2                 1 
0.895029646108037 0.895586927624849 0.896949551462331 0.897572079590053 
                1                 1                 1                 1 
0.897636798915308 0.898824108631426 0.899018226205464 0.902224675145764 
                1                 1                 1                 1 
 0.90388137138137  0.90442181680672 0.904522947655554 0.904868531850856 
                1                 1                 1                 1 
0.905160140075085 0.905199131734037 0.907908603214167 0.909985222888397 
                1                 1                 1                 1 
0.910369634704683 0.911358324634709 0.913417656302524 0.913442355343472 
                1                 1                 1                 1 
0.914307554199252 0.914906231894298 0.915005006079473 0.916083816009661 
                1                 1                 1                 1 
0.916821997818062 0.918738165713602 0.922347055027604 0.922722689357831 
                1                 1                 1                 1 
0.923638150290761 0.923652303739677 0.923993749516485 0.924533514811105 
                1                 1                 1                 1 
 0.92599045709692 0.926698046891224  0.92738734016936 0.927749112970918 
                1                 1                 1                 1 
0.929156654982786 0.929449821044403 0.931717468279045 0.932154940125562 
                1                 1                 1                 2 
0.934154831810681 0.935250813364141 0.935381498883791 0.935513973972908 
                1                 1                 1                 1 
0.936393826004722 0.937070644423922 0.939900007412363 0.941057195281254 
                1                 1                 1                 1 
0.941736997115192  0.94368595285946 0.943752748312622 0.943862472006647 
                1                 1                 1                 2 
0.944317018423498 0.945532123516936 0.945776091661955 0.946462096986349 
                1                 1                 1                 1 
0.949054041044226  0.95084593131949 0.951355920183733  0.95685018419563 
                1                 1                 1                 1 
 0.95905223165969 0.959867998806135 0.962093477219855 0.962432839898271 
                1                 1                 1                 1 
 0.96298289106909 0.964407547069204 0.965845502646825 0.970318631551722 
                1                 1                 1                 1 
0.973900838979688 0.973968772650075 0.974844088071628 0.977686214244416 
                1                 1                 2                 1 
 0.97803666052813 0.978685992340487 0.980275969155502 0.980716020907018 
                1                 1                 1                 1 
 0.98109326655663  0.98291961454063 0.983203197778922 0.986080197106396 
                1                 1                 1                 1 
0.987462962809093  0.98798219761531 0.988778254298348 0.990112883629133 
                1                 1                 1                 1 
0.990466191421899 0.990801843714705 0.990993793684525 0.995690103399442 
                1                 1                 1                 1 
0.997262509714786 0.997800602576348  0.99900850683577 
                1                 1                 2 
print(paste("Media:", media))
[1] "Media: 266.367857142857"
print(paste("Mediana:", mediana))
[1] "Mediana: 270.5"
print(paste("Moda:", moda))
[1] "Moda: 0.71945240936513"
print(paste("Varianza:", varianza))
[1] "Varianza: 23290.9020061334"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 152.613570845234"
print(paste("Rango:", rango))
[1] "Rango: 1"   "Rango: 531"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.17946448700023"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0.00149753601147101"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
   25%    50%    75% 
135.75 270.50 397.25 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
    5%    10%    15%    20%    25%    30%    35%    40%    45%    50%    55% 
 26.95  54.90  82.00 108.80 135.75 161.70 188.65 216.60 243.55 270.50 288.45 
   60%    65%    70%    75%    80%    85%    90%    95% 
316.40 342.35 369.30 397.25 425.20 451.15 479.10 505.05 

De este histograma, se infiere que la distribución de esta variable no es normal, y además, está sesgada hacia la derecha.

Para Recall:

library(e1071)  
library(dplyr)  

variable <- dataset$Recall

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
  hist(frecuencia, main="Distribución de la Variable Recall", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
 0.30009428510314 0.300947538000828 0.301095573634031 0.302673945861008 
                1                 1                 1                 1 
0.303054288755216 0.305489113540342 0.306204299579428 0.306326928355505 
                1                 1                 1                 1 
0.306946674789485  0.30709182881942 0.308194627511633 0.308472181743275 
                1                 1                 1                 1 
0.310020694366942 0.310285372058468 0.311863365422707  0.31228665435664 
                1                 1                 1                 1 
0.313381266100835 0.313529341642321  0.31634646742973  0.31651647525187 
                1                 1                 1                 1 
0.317813431934026 0.319275703908626 0.320418834551685  0.32166905364354 
                1                 1                 1                 1 
0.325213172803998 0.327250974327967 0.327297208802438 0.327621673023629 
                1                 1                 1                 1 
0.330729959850104 0.331437909296931 0.333730208675307 0.334985320061775 
                1                 1                 1                 1 
0.335158208024782  0.33579476700947 0.336648514131231 0.338032424376033 
                1                 1                 1                 1 
0.340491114613012 0.340664366456245  0.34166729024344 0.343542258315292 
                1                 1                 1                 1 
 0.34372031553335 0.345986401268056 0.346206890898169 0.346510691049042 
                1                 1                 1                 1 
0.349705365173279 0.350198322193356 0.350243064358559 0.350621532680557 
                1                 1                 1                 1 
0.351031284757532  0.35115709341891 0.352923528431725 0.353367452581495 
                1                 1                 1                 2 
0.353803452693314 0.354354534270123 0.356126009857332 0.362023299778775 
                1                 1                 1                 1 
0.362502667167901 0.366779494119247 0.371262578064676  0.37132467164621 
                1                 1                 1                 1 
0.373755445575599 0.376484947216735  0.37769866915392 0.378058548624894 
                1                 1                 1                 1 
0.380141346646134 0.381297272140368 0.382951836518706 0.384145060384403 
                1                 1                 1                 1 
0.384390891482583 0.384717500339635 0.386044474925771 0.386102306586622 
                1                 1                 1                 1 
0.387057879300357 0.387374569776794 0.387885150333857 0.391456640676424 
                1                 1                 1                 1 
0.393679854099785 0.393992395631593 0.394104590585685 0.395620632555821 
                1                 1                 1                 1 
0.397437690941987 0.398387077304853 0.398562064224873  0.39949598665542 
                1                 1                 1                 1 
0.399815900857336 0.399995201110587 0.400013172937588 0.402873896711747 
                1                 1                 1                 1 
0.403112130995279 0.404157178583581 0.407901530224941 0.412017455524236 
                1                 1                 2                 1 
0.413170005365873 0.413889820665996 0.416024845874109 0.416802141189127 
                1                 1                 1                 1 
0.416867162123039 0.422655240474079 0.430295128427344 0.433075354848609 
                1                 1                 1                 1 
0.434115062014378  0.43623668569341 0.437083158893989   0.4378479931174 
                1                 1                 1                 1 
0.439450692425837 0.440332160869882 0.440918475475703 0.442256163760261 
                1                 1                 1                 1 
0.443276076340099 0.444953066447599 0.446217906803615  0.44642982578555 
                1                 1                 1                 1 
0.447493474707042 0.448395838289061 0.451018475423518 0.452524787978493 
                1                 1                 1                 1 
0.454596948074106 0.455453109485324 0.457766887604736   0.4582202984712 
                1                 1                 1                 1 
0.459424815272247 0.459764754445589 0.460073745722526 0.462669026139233 
                1                 1                 1                 1 
0.468279239025455 0.469325305879022 0.469352176220871 0.469383991221932 
                1                 1                 1                 1 
0.472622544484617 0.472776708441332 0.473138221073358  0.47570096828361 
                1                 1                 1                 2 
0.480325054233605 0.481534428121966 0.481679248223263 0.481933485469983 
                1                 1                 1                 1 
 0.48731487370958 0.489275300469168   0.4899865663127 0.492292670533524 
                1                 1                 1                 1 
0.492766821978793  0.49303729777595  0.49331869047463 0.495131910690187 
                1                 1                 1                 1 
0.496703149236099 0.497735120783919 0.497747246180997 0.498991865049262 
                1                 1                 1                 1 
0.500048488868109 0.501186717525906 0.501883806473122 0.502219457236416 
                1                 1                 2                 1 
0.502471340380858 0.503353153969994 0.505316027546395 0.506233577442335 
                1                 1                 1                 1 
0.506528495357909  0.50670334583356 0.506711034300283  0.50863654604761 
                1                 1                 1                 1 
0.509576911860177 0.509695974567712 0.509860369295665 0.511633274546046 
                1                 1                 1                 1 
0.512041010183235 0.514419449144749 0.517852246544375 0.518304700541818 
                1                 1                 1                 1 
  0.5193435423096 0.519776702164147 0.520939140634345 0.521389104810515 
                1                 1                 1                 1 
0.522310756682782 0.523206772824797 0.525046990873517 0.525168992761684 
                1                 1                 1                 1 
0.532095289347036 0.536141882738365 0.538270972978154 0.538422916606904 
                1                 1                 1                 1 
0.539713585184299 0.540217147220861 0.541634545945947   0.5421142225165 
                1                 2                 1                 1 
0.543093927321355 0.544174373778636 0.547135274120212 0.548339904285189 
                1                 1                 1                 1 
0.549920540779009 0.550469858879484 0.551100867791909 0.552035326130685 
                1                 1                 1                 1 
0.552163743160299 0.553343993586505 0.555215609738278  0.55597652378296 
                1                 2                 1                 1 
0.557450191429307 0.558095019605357 0.558337115232642 0.558869279191024 
                1                 1                 1                 1 
0.559820696406339  0.56020684648164 0.560217506434431 0.562187020914085 
                1                 1                 1                 1 
0.562730935543721 0.564122637774235 0.565365834070355 0.568687218131486 
                1                 1                 1                 1 
 0.56894469909006 0.569858333315846 0.570578354776119 0.571354163818953 
                1                 1                 1                 1 
0.571715994288897 0.576596420285023  0.57848563785151 0.578603705068152 
                1                 1                 1                 1 
0.581245160458027 0.582011297842846 0.583002823078408 0.583571886169296 
                1                 1                 2                 1 
0.585280121722701 0.585308946001672 0.586740226426662 0.589549872443045 
                1                 1                 1                 1 
0.591553102332715 0.593263453131233 0.593613595770119 0.595423982089347 
                2                 1                 1                 1 
0.600091414690503 0.600951754173104 0.601370536923545 0.601689654359307 
                1                 1                 1                 1 
0.602910395213793 0.602971201546628 0.603672193703571 0.605629932838136 
                1                 1                 1                 1 
0.605897119965935 0.607404871643624 0.608308945218697 0.610830624441542 
                1                 1                 1                 1 
0.611879147119324 0.613371397787293 0.613823338758596 0.614544819427749 
                1                 1                 2                 1 
 0.61780113483728 0.619365556268879 0.620389723611506   0.6205970313025 
                1                 1                 1                 1 
0.620966106217324 0.621765409281863 0.623872923545775 0.624866611617453 
                1                 1                 1                 1 
0.628991787710556 0.630597262914087 0.631666879878563 0.632882226240779 
                1                 1                 1                 1 
0.633505890440654 0.633790427822472 0.633830074527579 0.636623102622106 
                1                 1                 1                 1 
0.638385205181203 0.638853948797141 0.640200345658322 0.641339466767048 
                1                 1                 1                 1 
0.642228482254716 0.644627836000827 0.645005209113213  0.64566982831985 
                1                 1                 1                 1 
0.647686795972563 0.648277896502272 0.649279349249706 0.650280801997141 
                1                 1                10                 1 
0.650422499808295 0.650436987649292 0.652158765545885 0.653818582537315 
                1                 1                 1                 1 
0.654170535414452 0.657790397466061 0.657892823540526  0.66110333189863 
                1                 1                 1                 1 
0.661688869658387 0.662572369398805 0.663322596090684 0.664118924617526 
                1                 1                 1                 1 
0.664907233357897  0.66502174710503 0.665803619535722 0.670761806761934 
                1                 1                 1                 1 
0.671656374888466 0.673370640135754 0.673777230783435  0.67898532514331 
                1                 1                 1                 1 
0.679193368687003 0.680117208770364 0.681137632960184 0.682603999422606 
                1                 1                 1                 1 
0.687598039750608 0.690396178375031 0.691049677515298 0.694851820183462 
                1                 1                 1                 1 
0.695559718716929 0.698564152827598 0.698677845696973 0.703985810226824 
                1                 1                 1                 1 
0.704039920714186 0.704095320463192 0.704808879594252 0.706062184268618 
                1                 1                 1                 1 
0.706327320695587 0.707135605092435  0.70753912261588 0.710105351917463 
                1                 1                 1                 1 
0.712112065491924 0.713791212280962  0.71549265476515 0.715562553845977 
                1                 1                 1                 1 
0.716592172433977 0.720751916760163 0.722060013535623 0.722445167230365 
                2                 1                 1                 1 
0.724045474616883 0.725426485576906 0.728801427841373 0.729522879966221 
                1                 1                 1                 1 
0.734462335877209 0.735640285232072 0.735689549096198 0.736384170711608 
                1                 1                 1                 2 
0.737348703952582 0.738364024994745 0.738614757765247 0.740690387824215 
                1                 1                 1                 1 
0.741645253160414 0.742898315124021 0.744054582210181  0.74516829501461 
                1                 1                 1                 1 
0.745267232486679  0.74583162221832 0.748333229523091 0.748430628484221 
                1                 2                 3                 1 
0.750904455033141  0.75138282281562 0.752075670400539 0.752521119146551 
                1                 1                 1                 1 
 0.75347221219337 0.756147832334094 0.756604154014358 0.759641751595513 
                1                 1                 1                 1 
 0.76014743751909 0.760978360969038 0.763703808190748 0.766469789504745 
                1                 1                 1                 1 
0.766620335332633  0.76800085270604 0.771076635676103 0.771891206875244 
                1                 1                 1                 1 
0.773984447814506 0.774279587221267 0.774469240217031 0.775068969670795 
                1                 1                 1                 1 
0.775734232914575 0.777832054856382 0.780612939444825  0.78091348655227 
                1                 1                 1                 1 
0.781405429701392 0.781791965046166 0.781883512944496 0.784744978668458 
                1                 1                 1                 1 
0.784772702075976 0.791778351074365 0.792699964144032 0.793910103850677 
                1                 1                 1                 1 
0.794883541219001 0.794960534086689 0.795404945187269 0.798205964022234 
                1                 1                 1                 1 
0.799132235444023 0.799244818297832 0.799766842754613 0.802831822760403 
                1                 1                 1                 1 
0.805500264819134  0.80589487038876 0.810203009588963 0.810421441284614 
                2                 1                 1                 1 
0.816508662993071 0.817018220692632 0.818333292367463  0.81863283930645 
                1                 1                 1                 1 
0.823211084617686  0.82405166388834 0.825824633465893 0.827399545579878 
                1                 1                 1                 1 
0.827985481342916 0.829349529765124 0.830117144994107 0.831143377630128 
                1                 2                 1                 1 
0.832705546446774 0.832726453175548 0.833258733964388 0.833331268823409 
                1                 1                 2                 1 
0.835169456258302  0.83628115295691 0.837297339962543 0.838245947475349 
                1                 1                 1                 1 
0.839110748229967 0.840138837685025 0.841045037313281  0.84119931174307 
                1                 1                 1                 1 
0.841793964706934 0.842742305282195 0.846255852104817 0.846263286499686 
                1                 1                 1                 1 
0.846925299023114 0.847276704341455 0.848238889309038 0.849632680203886 
                1                 1                 1                 1 
0.851284360101145 0.852252730243205 0.852289611944555 0.853356855992419 
                1                 1                 1                 1 
0.854816581401868 0.855200011797718 0.855947463784584 0.856160881143524 
                1                 1                 1                 1 
0.858866238362847 0.862437920307819 0.862770955286764 0.863106045375653 
                1                 1                 1                 1 
0.864875843618796 0.865008876155418 0.865764647006456  0.86778663895343 
                1                 1                 1                 1 
0.874838797785159 0.875525920771496 0.875695661567795 0.875774356068938 
                1                 1                 1                 1 
0.876653268954906 0.878695151819041 0.879263245474412  0.88355497335631 
                1                 1                 1                 1 
0.883901217900473 0.884836158019536 0.887536944649202 0.889898331512388 
                1                 1                 1                 1 
0.890554764836277 0.891923054092935 0.892145007774412 0.892878197944942 
                1                 1                 1                 1 
 0.89294257888873 0.893629462721039 0.895243600783927 0.897649445193267 
                1                 2                 1                 1 
0.897773376868795 0.898521141133955 0.900293636362899 0.904483265760182 
                1                 1                 1                 1 
0.905904001937186   0.9067392481542 0.908978411753379 0.911589015426441 
                1                 1                 1                 1 
0.913963406712732  0.91610971654504 0.916220333504249 0.918425334090242 
                1                 1                 1                 1 
0.921882570616077 0.922061356185779 0.923067924628666  0.92309879617721 
                1                 1                 1                 1 
0.923150501845322 0.924310501367514 0.924790759240532  0.92516314363679 
                1                 1                 1                 1 
0.925866011773276 0.928992423272387 0.931717315100089 0.934277701492748 
                1                 1                 1                 1 
0.935529155645733 0.936960200698074 0.939300863303366 0.941644665088845 
                1                 1                 1                 2 
0.942240090192393 0.942767360672806 0.942898502501786 0.943671717259235 
                2                 1                 1                 1 
0.948335847902247 0.948467824711061 0.950459637542298 0.959207998133248 
                1                 1                 1                 1 
0.959907023365879 0.960591114974155 0.960829465677778 0.962519559205284 
                1                 1                 1                 1 
 0.96338161817513 0.965321419402707 0.965540895411937 0.965650016151784 
                1                 1                 1                 1 
0.966000867253282 0.968542358039492 0.968580645104191 0.969143180268723 
                1                 1                 1                 1 
0.969233000528353    0.969759870839 0.970213613326667 0.970452860691743 
                1                 1                 1                 1 
0.970553884739739 0.972094923083813  0.97243888285924 0.972794839785315 
                1                 1                 1                 1 
0.973937845177244 0.974449468621312 0.974812184982392  0.97482019301586 
                1                 1                 1                 1 
0.974854891543076 0.976233253590074 0.976492170106485  0.98193611067145 
                1                 1                 1                 1 
0.983209676295449 0.984115535594053 0.985286780622366 0.986517540508401 
                1                 1                 1                 1 
 0.98669116471388 0.986800612254275 0.986824485733606 0.986834770414881 
                1                 1                 1                 1 
0.988809214247325 0.991625176308914 0.993929531094954 0.995278510796075 
                1                 1                 1                 1 
0.995693872229789 0.996373505776166 0.998474598977385 
                1                 1                 1 
print(paste("Media:", media))
[1] "Media: 266.821428571429"
print(paste("Mediana:", mediana))
[1] "Mediana: 271"
print(paste("Moda:", moda))
[1] "Moda: 0.649279349249706"
print(paste("Varianza:", varianza))
[1] "Varianza: 22891.4134934833"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 151.299086228183"
print(paste("Rango:", rango))
[1] "Rango: 1"   "Rango: 531"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.16814930781372"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: -0.0094400805535875"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
   25%    50%    75% 
137.75 271.00 395.25 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
    5%    10%    15%    20%    25%    30%    35%    40%    45%    50%    55% 
 28.95  55.90  83.85 110.80 137.75 164.70 191.65 218.60 243.55 271.00 290.45 
   60%    65%    70%    75%    80%    85%    90%    95% 
317.40 341.35 369.30 395.25 422.20 450.00 477.10 503.05 

De este histograma, se infiere que la distribución de esta variable no es normal, y además, está sesgada hacia la derecha.

Para F1_Score:

library(e1071)  
library(dplyr)  

variable <- dataset$F1_Score

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
  hist(frecuencia, main="Distribución de la Variable F1_Score", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
 0.40000698085322 0.400884293251787 0.401195281131442 0.403188085401008 
                1                 1                 1                 1 
0.404991965336315 0.405018209126114 0.405432496948223  0.40598726599507 
                1                 1                 1                 1 
0.406850790072444 0.407294062886432 0.408247332406807 0.408628867643251 
                1                 1                 1                 1 
0.409066410528685 0.409236935014785 0.410874424627438 0.411477379862372 
                1                 1                 1                 1 
0.413147997265005 0.413455533497233 0.415116048375538 0.418689455676035 
                1                 1                 1                 1 
0.420205842324678 0.422542654239345 0.423362810012599 0.423387592396678 
                1                 1                 1                 1 
 0.42421049611582 0.425453378924135 0.431001232994777 0.431101479471837 
                1                 1                 1                 1 
0.432780652000583 0.433705646408463 0.433951393688029  0.43463929553507 
                1                 1                 1                 1 
0.437515777445708 0.438403807965173 0.439877995465763 0.439938836748534 
                1                 1                 1                 1 
0.440184167215163 0.440353548380421 0.440501528010293 0.441011920185975 
                1                 1                 1                 1 
0.441075231600147 0.441228206634377  0.44140455556769  0.44142754378876 
                1                 1                 1                 1 
0.442295167385887  0.44269497110406  0.44446325354492  0.44535016831244 
                2                 2                 1                 1 
0.445419836385873 0.446183001628524  0.44618768023898 0.447073489790274 
                1                 1                 1                 1 
0.448689507121743 0.450132602506414 0.453030968190711 0.455240191649485 
                2                 1                 1                 1 
 0.45557528983082 0.456950762093002 0.460823738531896 0.461135860523762 
                1                 1                 1                 1 
0.461509578439885 0.461540777550154 0.463235930864683 0.463543482642255 
                1                 1                 1                 1 
0.466259118046662 0.467982102836479 0.469236785307351  0.47032234340814 
                2                 1                 1                 1 
0.470530780090132 0.476720080733451 0.478048401897368 0.479029017147456 
                1                 1                 1                 1 
0.484194710916109 0.485705178888599  0.49095704488006 0.492897167558632 
                1                 1                 1                 1 
 0.49388602960216 0.494363924907829 0.495695357524815 0.496219243671846 
                1                 1                 1                 2 
0.496277568562736  0.49681768063323 0.497821202158955 0.499170694085775 
                3                 1                 1                 1 
0.499448906179133 0.500392782400636 0.501928603630441  0.50301634462327 
                1                 1                 1                 1 
0.507551953443569 0.507553367144674 0.507618809207326 0.508968380653962 
                1                 1                 1                 1 
0.510065317842061 0.511388022940746 0.512633443415351 0.512752228489194 
                1                 1                 1                 1 
0.514555951042986 0.516317840762136 0.516985119940174 0.519395283375662 
                1                 1                 1                 1 
0.519562201880081 0.520169210720576 0.521352508314721 0.521579580481206 
                1                 1                 1                 1 
0.522083645498558 0.522589830039382  0.52319976322408 0.523751268301692 
                1                 1                 1                 1 
0.526981539141917 0.528643889795899 0.528947582221837 0.530600439748322 
                1                 1                 1                 1 
0.531229367798756 0.531732353937881 0.533416782848902 0.534576089971027 
                1                 1                 1                 1 
0.535675198749803 0.537325277490099 0.537758896452381  0.53824999727041 
                1                 1                 2                 1 
0.539210908185286 0.540522022555801 0.540984042997572 0.544897891154121 
                1                 1                 1                 1 
  0.5449003767957 0.544922105021009 0.545213247988526 0.546038009931118 
                1                 1                 1                 1 
0.547211388499727 0.548535862167932  0.54902575622188 0.549030165245925 
                1                 1                 1                 1 
0.549405241665454 0.550280739275499 0.550535827414661 0.551860923507765 
                1                 1                 1                 1 
0.551963430113629 0.555226985293265 0.555745869565029 0.556141958791138 
                1                 1                 1                 1 
0.558437190816231 0.558565757895184 0.558781016155214  0.55919568253328 
                1                 1                 1                 1 
0.560441216714525 0.561120253640564 0.561312108629316 0.561707117375364 
                1                 1                 1                 2 
0.562483796822184 0.562565618989819  0.56265775225844 0.563167623651069 
                1                 1                 1                 1 
0.564442953605315 0.565791465079512 0.566711665653827 0.569483455822002 
                1                 1                 1                 1 
0.571454994755624  0.57247699893835 0.572579637426207  0.57351246777757 
                1                 1                 1                 1 
0.574027319177462 0.575429866247316 0.577935947323558   0.5783744741844 
                1                 1                 1                 1 
0.580627646700588 0.581758543384258 0.582365507353016 0.582519231781769 
                1                 1                 1                 2 
0.584065959713285 0.584677499008447 0.585884125193481 0.587666793526212 
                1                 1                 1                 1 
0.587744436528189 0.588296084934649 0.592697291581572 0.593816407452456 
                1                 1                 1                 1 
0.594707080105205 0.595174371017049 0.595177080413819 0.595983549655547 
                1                 1                 1                 2 
0.596045525218025 0.599314619869363 0.599473694289227 0.600177037502119 
                1                 1                 1                 1 
0.600429979401262 0.601366272561906 0.602323945339451 0.605143166863294 
                1                 1                 1                 1 
0.607205171346933 0.607914500771631 0.610312320571697 0.611775102071414 
                1                 1                 1                 2 
0.612273495241862 0.612562796330329 0.612654969275833 0.614131585102666 
                1                 1                 1                 1 
0.616256096284892 0.621008328276611 0.621069351949947 0.621568462129325 
                1                 1                 1                 1 
0.621744519656064 0.622667763058077 0.623519964255731 0.624352628207688 
                1                 1                 1                 1 
  0.6252813570799 0.628310625921937 0.629679258661833 0.630613023114481 
                1                 1                 1                 1 
0.632695653950159 0.633538283015073 0.633642963387325 0.634619721476439 
                1                 1                 1                 1 
0.635115623912816  0.63563844596285 0.635917120616753 0.637932209193978 
                1                 1                 1                 1 
0.638567427131722 0.639421190585461 0.642160601416955 0.642716431344322 
                1                 1                 1                 1 
0.644891014520019 0.645647243090211 0.645802632025596 0.646714910796752 
                2                 1                 1                 1 
0.647174857020461 0.649939497089375 0.651000318461368 0.651562996699613 
                1                 1                 1                 1 
0.653577518208166 0.653637182136359 0.654910505720852 0.655136911262616 
                1                 1                 1                 1 
0.656560800222002 0.657366600058087 0.659211356556704 0.659407735842008 
                1                 1                 1                 1 
0.659660127759558 0.660083339653381 0.660149675579569 0.660412583625255 
                2                 1                 1                 1 
0.660641991403966 0.662596796888922  0.66352636074983 0.665376283270681 
                1                 1                 1                 1 
0.665527308888847 0.666351672703827 0.670152547685734 0.670776467817553 
                1                 1                 1                 1 
0.672607253840593 0.675364309958092 0.677029686287872 0.678543111843535 
                1                 1                 1                 1 
0.679785853684102 0.684352732069662 0.684553012586172 0.689823818535334 
                1                 2                 1                 1 
0.690393620907848 0.691056795987724 0.694657437629899 0.697755251729417 
                1                 1                 1                 1 
0.700067651245976 0.701578745578078 0.701879483530924 0.702877358982717 
                1                 1                 1                 1 
0.703380492053175 0.704152262777101 0.704235788043231 0.704683038375267 
                1                 1                 1                 1 
0.705334333354634 0.708312678524061 0.708636344236008 0.708960009947956 
                1                 1                10                 1 
0.709003395825834 0.710804839842775 0.711220596628357 0.711534742468123 
                1                 1                 1                 1 
0.712869414500128 0.713506108651353 0.716606479733017 0.719502439849589 
                1                 1                 1                 1 
0.721332288927804 0.721393959608547 0.722999165953428 0.723456731641605 
                1                 1                 1                 1 
0.724543002302849 0.725056578560538 0.726552379668219 0.726698175462319 
                1                 1                 1                 1 
0.727858189646708 0.729051497796138 0.731624245431127 0.732022713849863 
                1                 1                 1                 1 
0.734127065903257 0.734402301743805 0.735435570967961  0.73640697696337 
                1                 1                 1                 1 
0.738037210427584 0.739708414735043 0.743047589886249 0.746021439314654 
                1                 2                 1                 1 
0.747284052707164 0.748570227932908 0.749755634082558 0.750228152638818 
                1                 1                 1                 1 
0.750669345854456 0.752161903935344 0.752551522665641 0.753672393690818 
                1                 1                 1                 1 
0.754382700396783 0.757181959556493 0.758111126132656 0.758293183594181 
                1                 1                 1                 1 
0.758600969621622 0.759426752290229 0.760932327579894 0.762182320335625 
                1                 1                 1                 1 
0.763382733594047 0.764039034830462 0.764651609857392 0.766004450247691 
                1                 1                 1                 1 
0.766328053009255 0.767975010932427 0.769780291555434 0.770070164711525 
                1                 1                 1                 1 
0.771715720021782 0.772284271031182 0.772775469429766  0.77418926697416 
                1                 1                 1                 1 
0.774245850918405 0.774924459764199 0.777055873968752 0.778148331673695 
                1                 1                 1                 1 
0.778851352731026 0.779369292182584 0.779434794597032 0.781824568920025 
                1                 1                 1                 1 
0.782612948137561 0.785040638379135 0.788990804471257 0.789102892071213 
                1                 1                 1                 1 
0.789593394746129 0.792479642216724 0.792605203295632 0.792790412119573 
                1                 1                 1                 1 
0.793104228714603 0.794037690832965 0.794053638084734 0.795706461184462 
                1                 1                 1                 1 
0.796608552548392 0.797010573039914 0.797181366876321 0.797828315082054 
                1                 1                 1                 1 
0.798531630993381 0.799877828516101 0.802694484027813 0.802887489200324 
                1                 1                 1                 1 
0.803476298815017 0.803621796525339 0.803723001158848 0.804187250484945 
                1                 1                 1                 1 
0.804411951435276 0.805615772831529 0.806164469798102 0.808067131268184 
                1                 1                 1                 1 
0.811266329933141 0.813178977584725 0.815244188214621 0.815415353476635 
                1                 1                 1                 1 
0.816170834484277 0.816369754306094 0.816757256351971 0.816784575336237 
                1                 1                 1                 1 
0.817693687082755 0.818325629145782 0.819369297092431 0.820683756650484 
                1                 1                 1                 1 
0.820701916954156 0.821287657709098 0.822219867777431 0.822732656816467 
                1                 1                 1                 1 
0.822922606026029 0.823276498170092 0.823977921927226 0.824438200019757 
                1                 1                 1                 1 
0.825259393137493 0.825592497083566 0.827572799859108 0.828431634026876 
                1                 1                 1                 1 
0.828595981440999 0.828654498442745 0.829838267174859  0.83107236839353 
                1                 1                 1                 1 
0.831243770712118 0.834066197412947 0.834068690710001 0.836234056969234 
                1                 1                 1                 1 
 0.83738863699349 0.837606876452798 0.839440629435027 0.839619430354168 
                1                 1                 1                 1 
0.839640084871699 0.840666359245355 0.841921137000876 0.842730990900764 
                1                 1                 1                 1 
0.842750436012415  0.84323389043594 0.845351912319452 0.845728896200763 
                1                 1                 1                 1 
0.849030609805739 0.850563879017991 0.851048195437504 0.852548955809248 
                1                 1                 1                 1 
0.854038100241141 0.855229192698352 0.855403169513159 0.856510798558469 
                1                 1                 1                 1 
0.857381574700576 0.858612031861856 0.858664436845303 0.859328050309517 
                1                 1                 1                 1 
0.859909029719551 0.862673689511132 0.863685743974203 0.866815145886792 
                1                 1                 1                 1 
0.868379030455334 0.869175986294775 0.870242950645142 0.870255905490464 
                1                 1                 2                 1 
0.871723391356635   0.8724322160514 0.873575708991811 0.874934921554822 
                1                 1                 1                 2 
0.875654868143688 0.877744870324821 0.878008838314823 0.880002089058209 
                1                 1                 1                 1 
0.882288727116068 0.882696785459093 0.883054191097398  0.88399903181609 
                1                 1                 1                 1 
0.884016111816843 0.884242542320022 0.886527148604751 0.888475411354697 
                1                 1                 1                 1 
0.888963837124324 0.890067679903382 0.890276885209351 0.892833017740417 
                1                 1                 1                 1 
0.893098567951216  0.89379028302506 0.894845942408205 0.895249398474369 
                1                 1                 1                 1 
0.896503791923933 0.897133358743649 0.899698226072963  0.90149555674631 
                1                 1                 1                 1 
0.902271776698391 0.902745024911082 0.903095100305815 0.903398396630806 
                1                 1                 1                 1 
0.903880963998656 0.906922808653137 0.909055227454315 0.912984411736885 
                1                 1                 1                 1 
0.913922334248756 0.914813962604338 0.915258567609683 0.915290062700893 
                1                 1                 1                 1 
0.917014542272407 0.917584282689507 0.919177455345347  0.92231617976163 
                1                 1                 1                 1 
0.925529850110234 0.925791659885387 0.926410271879703 0.926482027992689 
                1                 1                 1                 1 
0.927511463560749 0.929014367106105 0.929796294897864 0.932870913360421 
                1                 1                 1                 1 
0.933476754364006 0.934245710331597 0.934513320989888 0.937207653491902 
                1                 1                 1                 1 
  0.9387515121746 0.940576537414281 0.941064417127737  0.94116411804949 
                1                 1                 1                 1 
0.943652236288756 0.944703108330121 0.944937093220194 0.948273066323956 
                1                 1                 1                 2 
0.948729198309135 0.952459965078014 0.952596712657946 0.956266377315056 
                1                 1                 1                 1 
0.956909258868371 0.957483712009278 0.959626304879657 0.959754917541803 
                1                 1                 1                 1 
0.961768372881356 0.963441087670175 0.964470712301865 0.964672487520204 
                1                 1                 1                 1 
0.966669149616582 0.966841755269848 0.968040237354037 0.968254400265111 
                1                 1                 1                 1 
 0.97085393250734 0.970894426106072 0.971333071418557 0.971689010201504 
                1                 1                 1                 1 
 0.97454860905029 0.975917681628073 0.979009221672683 0.980107299879571 
                1                 1                 1                 1 
0.980221165153688 0.980839487230455 0.981122399019935 0.982154265835634 
                1                 1                 1                 1 
0.982405927245847   0.9838468977834 0.986204172663366 0.987115281033484 
                1                 1                 1                 1 
0.988221244565311 0.990915041657485  0.99440749423946 0.997694604099267 
                1                 1                 1                 1 
 0.99830941234177 0.998576978441294 0.999335567219974 
                2                 1                 1 
print(paste("Media:", media))
[1] "Media: 263.9875"
print(paste("Mediana:", mediana))
[1] "Mediana: 265.5"
print(paste("Moda:", moda))
[1] "Moda: 0.708636344236008"
print(paste("Varianza:", varianza))
[1] "Varianza: 23249.568716458"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 152.478092578763"
print(paste("Rango:", rango))
[1] "Rango: 1"   "Rango: 531"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.18497413441012"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0.0260643350153632"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
   25%    50%    75% 
132.75 265.50 395.25 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
    5%    10%    15%    20%    25%    30%    35%    40%    45%    50%    55% 
 28.95  53.90  80.00 105.80 132.75 159.70 185.65 212.60 238.55 265.50 284.45 
   60%    65%    70%    75%    80%    85%    90%    95% 
311.40 339.35 367.30 395.25 423.20 449.15 477.10 504.05 

De este histograma, se infiere que la distribución de esta variable no es normal, y además, está sesgada hacia la derecha.

Para Training_Time:

library(e1071)  
library(dplyr)  

variable <- dataset$Training_Time

#Frecuencia
frecuencia <- table(variable)

#Medidas de tendencia central
media <- mean(as.numeric(factor(variable)), na.rm = TRUE)   
mediana <- median(as.numeric(factor(variable)), na.rm = TRUE)
moda <- names(which.max(table(variable)))

#Medidas de dispersión 
varianza <- var(as.numeric(factor(variable)), na.rm = TRUE)
desviacion <- sd(as.numeric(factor(variable)), na.rm = TRUE)
rango <- range(as.numeric(factor(variable)), na.rm = TRUE)

#Curtosis y Asimetría
curtosis <- kurtosis(as.numeric(factor(variable)), na.rm = TRUE)
asimetria <- skewness(as.numeric(factor(variable)), na.rm = TRUE)

# Distribución de frecuencias usando gráfico de barras
  hist(frecuencia, main="Distribución de la Variable Training_Time", 
        xlab="Categorías", ylab="Frecuencia", col="gray")

#Percentiles y cuartiles
cuartiles <- quantile(as.numeric(factor(variable)), probs = c(0.25, 0.5, 0.75), na.rm = TRUE)
percentiles <- quantile(as.numeric(factor(variable)), probs = seq(0.05, 0.95, by = 0.05), na.rm = TRUE)

print("Frecuencia:")
[1] "Frecuencia:"
print(frecuencia)
variable
0.103201614730368 0.131257312692294 0.133702014876282 0.150394030084891 
                1                 1                 1                 1 
0.152974309812462  0.15538242928621  0.18130315509973   0.1938098531845 
                1                 1                 1                 1 
0.193861879201139  0.21616799285814 0.222361144373543 0.240396895130507 
                1                 1                 1                 1 
0.247127426114025 0.247508973835463 0.249272062913905 0.255544450327644 
                1                 1                 1                 1 
0.258972885631216  0.26002939784403 0.271066608015497 0.292420129784096 
                1                 2                 1                 1 
0.293019985094815 0.296289683348403 0.297264214745237 0.305384561909662 
                1                 1                 1                 1 
0.343110429360304 0.346190748132613 0.346712682149831 0.347808208738721 
                1                 1                 1                 1 
0.348050114118463 0.351339860007956 0.354747824690767 0.358549763512053 
                1                 1                 1                 1 
0.372467056234257 0.379195762287105 0.402861457377191 0.405730936131558 
                1                 1                 1                 1 
0.406567726875313 0.424209425288758 0.428381034980929  0.42944748244375 
                1                 1                 1                 1 
0.443529884242159  0.44807095631561 0.476334936740666 0.486803074438122 
                1                 1                 1                 1 
0.503134388957603 0.505410494529131 0.509272081932092 0.512225545070976 
                1                 1                 1                 1 
0.514370352676465 0.514972875189003 0.517007081986948 0.526384369683665 
                1                 1                 1                 1 
0.552566587745755 0.559504978659381 0.567268514237717 0.591203262242096 
                1                 1                 1                 2 
0.594792723407029 0.605998543487737 0.611827138690742 0.618784159244334 
                1                 1                 1                 1 
0.646805699790513  0.67015657730603 0.671257065322914 0.681354452133744 
                2                 1                 1                 1 
0.681674567994646 0.687466358016289 0.689899136066536 0.714882854315838 
                1                 1                 1                 1 
0.717409936533572 0.735426993298753 0.763751730293985 0.772027591948442 
                1                 1                 1                 1 
0.791995362528432 0.800705501062059 0.805986051464678 0.817537657353799 
                1                 1                 1                 1 
0.819917425560477 0.821650261405246 0.837314127929388  0.84503798038001 
                1                 1                 1                 1 
0.853086109936602 0.857011799624136 0.865412186564448 0.868382256052348 
                1                 1                 1                 1 
0.885105444784881 0.887329965088041 0.889972178678101 0.890700056103077 
                1                 1                 1                 1 
0.897675847110524 0.898793657692943 0.905587092486506 0.920049457960227 
                1                 1                 1                 1 
0.920706336561128 0.924197913255939 0.931669300026923 0.936470980231153 
                1                 1                 1                 1 
0.937588371862157 0.945366997037174 0.950130646739608 0.958103386638731 
                1                 1                 1                 1 
0.959908974168651 0.978844450417281 0.987798067345406 0.990716449365073 
                1                 1                 1                 1 
0.995905121357204  1.00469904100211  1.00782474137829  1.01009205282541 
                1                 1                 1                 1 
  1.0339881820648  1.05631593437139  1.06245415777288   1.0636025662695 
                1                 1                 1                 1 
 1.10179702507494  1.11695058740795  1.12439093116355  1.13148400436018 
                1                 1                 1                 1 
 1.13288619759514  1.13451711853438  1.13503597421736  1.14099165825782 
                1                 1                 1                 1 
 1.15200984857044  1.16921691930564  1.17167802158556  1.18018542080255 
                1                 1                 1                 1 
 1.18047089083467  1.18406961258571  1.19111278770312  1.19916093838228 
                1                 1                 1                 1 
 1.20778744795176  1.20995596757692   1.2238923074846  1.22615095640833 
                1                 1                 1                 1 
 1.23376511824655  1.23422854744996  1.23927936181837  1.24568288215601 
                2                 1                 1                 1 
 1.24868544005642  1.26097329204258  1.26364492808606  1.26691860296191 
                2                 1                 1                 1 
 1.30862721744649  1.32337786842713  1.33072941098717  1.33900477942555 
                1                 1                 1                 1 
  1.3511482314399  1.35666899898215  1.37238711085703  1.38991199793826 
                1                 1                 1                 1 
 1.40093239640245  1.40304940809738  1.41595462052285  1.43031081245929 
                1                 1                 1                 1 
 1.43100258824441  1.43279316618734  1.44083804751778  1.44867198708134 
                1                 1                 1                 1 
 1.44891224591412   1.4573613691973  1.45957693065228  1.46400556014702 
                1                 1                 1                 1 
 1.47714377581776   1.4799186063176  1.49996708153836   1.5039457897429 
                1                 1                 1                 1 
 1.51093217911236  1.52815847611959  1.55215230621511  1.56697853115621 
                1                 1                 1                 1 
 1.56971614190741  1.58185560526483  1.58610086516149  1.60152083124652 
                1                 1                 1                 2 
 1.60167099340982  1.60536044340423  1.61149457929847  1.62820923524225 
                1                 1                 1                 1 
 1.63798993394011  1.63800257492363  1.65599353126218  1.69353486175344 
                1                 1                 1                 1 
 1.69864419840162  1.70129405870311   1.7080794657083  1.70834221782386 
                1                 1                 1                 1 
 1.73856577704487  1.74286734538365  1.75352596692472  1.76586213258692 
                1                 1                 1                 1 
 1.76801662495987  1.77896121796036  1.78259484067046  1.78539266413266 
                1                 1                 1                 1 
 1.79091035301485  1.79444988221108   1.8028420970374  1.81901363574158 
                1                 1                 1                 1 
 1.82097499800903  1.83786440442691  1.83899864908412  1.83913083829735 
                1                 2                 1                 1 
 1.84106676752205  1.86012286021518  1.87087851742921  1.87654300313956 
                1                 1                 1                 1 
 1.90021457061565  1.92018958685945   1.9236489507098  1.92529376461198 
                1                 1                 1                 1 
 1.92830083026968  1.92994393115026  1.93528639255995  1.93613765548614 
                1                 1                 1                 1 
 1.95729837837687  1.96078246230466  1.96685724097516  1.98459427229596 
                1                 1                 1                 1 
 1.99788033807904  2.02125852683241  2.02620914704106  2.03340434506273 
                1                 1                 1                 1 
 2.03626095761429  2.03677064561267  2.04865363072197  2.04954194478539 
                1                 1                 1                 1 
 2.05764204447598  2.06104015166339  2.06924727946458  2.07179067056663 
                1                 1                 1                 1 
 2.07571800505294  2.07573210260073  2.09796571451339  2.11486769552448 
                1                 2                 1                 1 
 2.12454533431783  2.14424775096643  2.14656827950328  2.14890946199772 
                1                 1                 1                 1 
 2.15117564709982   2.1539960919204  2.15617417575337  2.17434220635067 
                1                 1                 1                 1 
 2.18799406596593   2.1994437288591  2.20679233692113  2.20692754919319 
                1                 1                 1                 1 
 2.21304596197863  2.21337836107097   2.2258352219907  2.24707520491689 
                1                 1                 1                 1 
 2.25472838388875  2.26632446993063  2.26971086906431  2.28890118356675 
                2                 1                 1                 1 
 2.30028996285762   2.3052873331885  2.32455056487853  2.32834527850804 
                1                 1                 1                 1 
 2.33034275949492  2.34385207272674  2.34578561347912  2.34631397824405 
                3                 1                 1                 1 
 2.34970771410474  2.35196188034675  2.37351032101775  2.37854663587949 
                1                 1                 1                 1 
 2.38486712340511   2.3867962923336  2.39353836574802  2.39862533413314 
                1                 1                 1                 1 
  2.4077052369302  2.43042133992784   2.4347191453638  2.43901695079977 
                1                 1                 9                 1 
 2.46244728470722  2.46758623023698  2.47170080529608  2.47423617589205 
                1                 1                 1                 1 
 2.48203937755313  2.48760023509025  2.49362860003354  2.49802343329229 
                1                 1                 1                 1 
  2.4991598640462  2.51342336550002  2.51358844669116  2.51481596421084 
                1                 1                 1                 1 
 2.55176128645625  2.55625065866607  2.55743800571582  2.56189370711525 
                1                 1                 1                 1 
 2.57699292591033  2.59828464679724  2.61906766850117  2.67120462454102 
                2                 1                 1                 1 
 2.69670887595814  2.70334068991957   2.7041290795276  2.70470354816498 
                1                 1                 2                 1 
 2.70823019216213  2.72608188637538  2.73631125628313  2.74745300577251 
                1                 1                 1                 1 
 2.76657344626814  2.77764685446781  2.77880884215344  2.79435595760341 
                1                 1                 1                 1 
 2.79825055926017  2.80068381339022  2.80804511210607  2.82824606354812 
                1                 1                 1                 1 
 2.85472517421617  2.86070098597088  2.87232961872088  2.87636576863677 
                1                 1                 1                 1 
 2.88186385786217   2.8830740568488  2.89917630269178   2.9027798035896 
                1                 1                 1                 1 
 2.90790678303318  2.91235434373815  2.91400911794203  2.92660116755023 
                1                 1                 1                 1 
 2.93039559628767   2.9386408866435    2.945425514316  2.95763494095778 
                1                 1                 2                 1 
 2.95793672233153  2.98292588281745  3.00491688448974   3.0064752732934 
                1                 1                 1                 1 
 3.01475215955936  3.01654288722169   3.0208015806677  3.02486238367861 
                1                 1                 1                 1 
 3.03658036908325  3.05200226563628  3.05729115185549  3.08076555003808 
                1                 1                 1                 1 
 3.08751738324782  3.09617169500574  3.09797199850578   3.1026995941289 
                1                 1                 1                 1 
 3.10845450099364  3.11413278865188  3.15088961463342  3.15117875065401 
                1                 1                 1                 1 
 3.15149167587522  3.15759257909201  3.17391178194432  3.18612120673007 
                1                 1                 1                 1 
 3.21353034862336  3.21610760145088  3.25925171802641   3.2783308881672 
                1                 1                 1                 1 
 3.28259375556649  3.31640705715322  3.31944944134713  3.32498313905811 
                1                 1                 1                 1 
 3.32744063920486  3.32771642976241  3.32932250964794   3.3315793100915 
                1                 1                 1                 1 
 3.34216957218303  3.34242154495539  3.34271088911103  3.34337679992136 
                1                 1                 1                 1 
 3.35126561017592  3.36934045225149  3.37202689885545  3.37255274283399 
                1                 1                 1                 1 
 3.38835646972128  3.40257161991408  3.40645288062031  3.41153233300996 
                1                 1                 1                 1 
 3.41922633645548  3.41944654901864  3.41990490803005  3.47142322966323 
                1                 1                 1                 1 
 3.48533148509903  3.48617348242238  3.49085515413861  3.51596544886987 
                1                 1                 1                 1 
  3.5282338911484  3.55518181329576  3.56060619652078  3.57625043670648 
                1                 1                 1                 1 
 3.60229105457534  3.60399079029013  3.60864486888651  3.65053160555338 
                1                 1                 1                 1 
 3.65252977386568  3.66901718626427  3.68428316254527  3.68433267381138 
                1                 1                 1                 1 
 3.69170052539085  3.70113665223498  3.71338782027632  3.72044671795186 
                1                 1                 1                 1 
 3.72142818210293  3.73404311399661  3.77630224330033  3.77877128113417 
                1                 1                 1                 1 
 3.78076797107481  3.78674962328856  3.78709485417382  3.79395360527857 
                1                 1                 2                 1 
 3.80953576202326  3.81068659354995  3.82053328390052  3.82478855597178 
                1                 1                 1                 1 
 3.82682064803088  3.83599009750686  3.87029958100203  3.88657995635889 
                1                 1                 1                 1 
 3.89869585399125   3.9075414996936  3.91760267333935  3.93816011648463 
                1                 1                 1                 1 
 3.95812259493144  3.98371458472476  4.00888809040625  4.01163666632501 
                1                 1                 1                 1 
 4.02480543197649  4.02708430349247  4.03293753052936  4.03377358064005 
                1                 1                 1                 1 
 4.03864396336903  4.04162889241962   4.0466072109253  4.04661841356993 
                1                 1                 1                 1 
 4.04767914628038  4.04800117577427  4.06118812057909  4.06421583742921 
                1                 1                 1                 1 
 4.09188792307895    4.103172145632  4.10479602984486  4.11182712447185 
                1                 1                 1                 1 
 4.12141118775722  4.12280698476579  4.12966793480824  4.13540591039791 
                1                 1                 1                 1 
 4.13575569266997  4.13991043626229  4.14598366264727  4.15010026353818 
                1                 1                 1                 1 
 4.15160694876649   4.1537805337125  4.15500995614283  4.17165093816983 
                1                 1                 1                 1 
 4.18135560631372  4.18485565132834  4.18940177225258  4.19124130790258 
                1                 1                 1                 1 
 4.20309869087374  4.20695937744435  4.20732906330082  4.21198393540346 
                1                 1                 1                 1 
 4.21652958435208  4.22045268097424   4.2366403939021   4.2388629545421 
                1                 1                 1                 1 
 4.24109217233057  4.25220085979973  4.25573525157659  4.27748236410526 
                1                 1                 1                 1 
 4.31299390657706  4.32479457092512  4.32868447365847  4.33682871710489 
                1                 1                 1                 1 
 4.35407217573482  4.35520666733998  4.36627826721504  4.36637343174145 
                1                 3                 1                 1 
 4.38295168919541  4.40871805682452  4.41676772763432  4.42628260094174 
                1                 1                 1                 1 
 4.43447575232511  4.44185783303472  4.44229068343379  4.48825795584601 
                1                 1                 1                 1 
 4.49709274237557  4.50002676955416  4.50209368626177  4.52182386310191 
                1                 1                 2                 1 
 4.53079212789707   4.5313628974699  4.55132930420894  4.55495879386257 
                1                 1                 1                 1 
 4.56196801435067  4.58379758933439  4.59046066820713  4.61162428667891 
                1                 1                 1                 1 
 4.61440680984358  4.63967260998531   4.6429065311358  4.65028975436543 
                2                 1                 1                 1 
 4.65280911433727  4.65895225882969  4.66461908011646   4.6727049300206 
                1                 1                 1                 1 
  4.6753721727072   4.6780901594207  4.69602963402608  4.69774707039145 
                1                 1                 1                 1 
 4.69879593901834  4.71429073462435  4.73910559899198  4.74109116821121 
                1                 1                 1                 1 
 4.76207964574915  4.79477824370523  4.80850871995124  4.81131239041315 
                1                 1                 1                 1 
 4.82046557018559  4.83216132811676  4.84203117982085  4.84357426910859 
                1                 1                 2                 1 
 4.85164580071009  4.85263997419144   4.8586394461046  4.86807630977026 
                1                 1                 1                 1 
 4.86957483390762  4.87162202545003   4.8759839206379  4.87918135404745 
                1                 1                 1                 1 
  4.8939384565786  4.90478431259755  4.91947931191695  4.94831054172878 
                1                 1                 1                 1 
 4.95153334582564  4.97859243654453  4.98646570952765  4.99783274592715 
                1                 1                 1                 1 
print(paste("Media:", media))
[1] "Media: 266.883928571429"
print(paste("Mediana:", mediana))
[1] "Mediana: 269.5"
print(paste("Moda:", moda))
[1] "Moda: 2.4347191453638"
print(paste("Varianza:", varianza))
[1] "Varianza: 23276.6609219269"
print(paste("Desviación Estándar:", desviacion))
[1] "Desviación Estándar: 152.566906378569"
print(paste("Rango:", rango))
[1] "Rango: 1"   "Rango: 532"
print(paste("Curtosis:", curtosis))
[1] "Curtosis: -1.17621642469571"
print(paste("Asimetría:", asimetria))
[1] "Asimetría: 0.00131602697981087"
print("Cuartiles:")
[1] "Cuartiles:"
print(cuartiles)
   25%    50%    75% 
136.75 269.50 398.25 
print("Percentiles:")
[1] "Percentiles:"
print(percentiles)
    5%    10%    15%    20%    25%    30%    35%    40%    45%    50%    55% 
 27.95  55.90  81.85 109.80 136.75 163.70 190.65 217.60 244.55 269.50 289.00 
   60%    65%    70%    75%    80%    85%    90%    95% 
315.40 342.35 370.30 398.25 425.20 453.15 479.10 505.05 

De este histograma, se infiere que la distribución de esta variable no es normal, y además, está sesgada hacia la derecha.

Como último paso, se realizan algunos análisis bivariados, que como lo indica su nombre, tienen como objetivo explorar las interacciones entre variables a través de gráficos o pruebas analíticas. Por supuesto, esta exploración debe ayudar a responder la pregunta formulada al inicio del EDA, por lo que se utilizarán las variables necesarias para sacar las conclusiones requeridas.

En base a esto, se generan gráficos de barras, diagramas de caja y bigote y dispersión:

library(ggplot2)
library(dplyr)

ggplot(dataset, aes(x = Framework, y = Accuracy, fill = Dataset_Type)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(title = "Precisión por Framework y Tipo de Dataset",
       x = "Framework", y = "Accuracy") +
  theme_minimal()

El gráfico de barras agrupadas, muestra la relación entre las variables Accuracy, Framework y Dataset_Type. Todos los frameworks utilizados presentan una precisión muy similar al trabajar con datos tabulares, situándose alrededor del 0.75-1.00. De este se puede inferir, que ninguno de ellos tiene una ventaja significativa sobre los demás en este tipo de datos; además, debido a su uniformidad, se puede afirmar que los cuatro frameworks son igualmente capaces de capturar la estructura de los datos tabulares, en términos de exactitud.

library(ggplot2)
library(dplyr)

ggplot(dataset, aes(x = Framework, y = Training_Time, fill = Framework)) +
  geom_boxplot() +
  labs(title = "Tiempo de Entrenamiento por Framework",
       x = "Framework", y = "Tiempo de Entrenamiento (s)") +
  theme_minimal()

Los diagramas de caja y bigote, muestran la relación entre las variables Training_Time y Framework. Al realizar la comparación con TensorFlow y PyTorch, que presentan tiempos de entrenamiento considerablemente más largos y variables, es evidente que Scikit-learn, ofrece tiempos mucho más eficientes y consistentes. Keras, aunque tiene una mayor variabilidad, también puede ser más eficiente que TensorFlow en ciertos casos. Sin embargo, Scikit-learn es el único framework que logra mantener una precisión alta sin alcanzar un coste significativo de tiempo, lo cual lo convierte en la mejor opción cuando el objetivo es conseguir resultados rápidos y precisos.

Analizando los diagramas con mayor profundidad, se puede afirmar que la mediana baja de Scikit-learn (sesgo positivo) y su menor dispersión (la caja es más estrecha) indican que, en general, este framework ofrece mejores y más rápidos tiempos de entrenamiento. Pues no sólo tiene tiempos más bajos en promedio, sino que estos también son menos variables, y por ende, la probabilidad de obtener tiempos de entrenamiento excesivamente largos, como sucede con TensorFlow o Pytorch, es menor.

library(ggplot2)
library(dplyr)

ggplot(dataset, aes(x = Accuracy, y = Training_Time, color = Framework)) +
  geom_point(size = 3) +
  labs(title = "Relación entre Precisión y Tiempo de Entrenamiento",
       x = "Precisión (Accuracy)", y = "Tiempo de Entrenamiento (s)") +
  theme_minimal()

El diagrama de dispersión, muetra la relación entre las variables Training_Time, Accuracy y Framework. En este caso, no se observa una correlación clara entre el tiempo de entrenamiento y la precisión de las IAS. Esto significa que invertir más tiempo en el entrenamiento de una inteligencia artificial, no necesariamente conlleva a un aumento en su precisión. Por lo que optar por frameworks que requieren más tiempo, sin una ganancia clara en precisión, no es nada eficiente y no debe ser el paso a seguir.

Antes de resolver la pregunta final, es importante acotar que toda la información necesaria para la resolución de la misma puede ser inferida a través de los gráficos realizados, por lo que no es necesario recurrir al uso de pruebas analíticas como ANOVA, t de Student, U de Mann- Whitney, Chi-Cuadrado, entre otras.

Ahora si, respondiendo a la pregunta problema, tras haber realizado numerosos análisis a lo largo de este EDA. Se puede afirmar que el framework más adecuado para trabajar con datasets tabulares es Scikit-learn, debido a que este maximiza la eficiencia en términos de tiempo de entrenamiento sin sacrificar precisión. Por lo que es sumamente recomendado para proyectos donde el tiempo de entrenamiento o sus recursos computacionales se conviertan en un factor crítico.